vmap-layout, a layout algorithm for drawing scientograms

Vmap-Layout, a Layout Algorithm for DrawingScientograms

Arnaud Quirin and Oscar Cordón

Summary We present in this chapter a drawing algorithm to represent graphicallyco-citation networks (scientograms). These networks have some interesting and un-usual topological properties which are often valuable to be visualized. In general,these networks are pruned with a network scaling algorithm, then visualized usinga drawing algorithm [7]. However, typical drawing algorithms do not work prop-erly, especially when the size of the networks grows. Edge crossings appear whilethe drawing space is not adequately filled resulting in an unsightly display. The ap-proach presented in this chapter is able to print the networks filling all the availablespace in an aesthetic way, while avoiding edge crossings. The algorithm is detailedand compared with the classical Kamada-Kawai drawing algorithm on several sci-entograms.

1 Introduction

Social networks have some interesting and unusual topological properties whichare often valuable to be printed graphically. However, the raw networks cannot beoften visualized easily, especially when their size grows proportionally with thenumber of data to be dealt with, and thus specific algorithms for simplifying suchlarge networks have been developed. Network scaling algorithms, whose goal is totake proximity data and to obtain structures revealing the underlying organization ofthose data, use similarities, correlations or distances to prune a network based on theproximity between a pair of nodes. One of the most known, the Pathfinder algorithm[10], is used frequently due to its various mathematical properties, including theconservation of the triangle inequalities among a path of any number of links, thecapability of modeling asymmetrical relationships, the representation of the most

European Centre for Soft Computing, Edf. Científico Tecnológico, Mieres, SpainPhone: +34 985456545, FAX: +34 985456699e-mail: {arnaud.quirin,oscar.cordon}@softcomputing.es

1

2 Arnaud Quirin and Oscar Cordón

salient relationships present in the data, and the fact that hierarchical constraintsin most cluster analysis techniques do not apply to Pathfinder Networks (PFNETs)[10].

The resulting network could then be graphically represented using a networkdrawing algorithm. This methodology ensures the network is represented in an aes-thetic way, usually by adding several spatial constraints, such as the minimizationof the edges crossings, the optimal distribution of the nodes over the space and theminimization of the length of the edges. The final goal of this methodology is togenerate a network having some properties. If the network represents the complextissue of relationships between individuals or organizations, and if its goal is thecomprehension of these relationships by a domain expert, we may be interested bysome specific properties. For instance, the backbone could be better highlighted ifit is drawn in the center, and minor links could be represented in the border of themap. The Kamada-Kawai [14] or the Fruchterman-Reingold [12] algorithm are usu-ally applied for this task.

There are some kinds of Social Network Analysis (SNA) applications whichcould benefit from such methodology, giving to the domain expert or even a simpleuser a simple access to the information contained in these networks. One of theseapplications is co-citation network analysis. Co-citation network models depict thecomplex tissue of relationships occurring in the scientific literature. The graphi-cal representation of these kinds of networks while preserving their information isstill a challenge. However, some work has been done using scientograms [7, 8],visual representations showing the spatial distribution of the scientific actors in agiven domain, where these actors can be as diverse as scientific categories, authors,journals or papers. They show also additional information about the relationshipsbetween them, for instance the proximity between two scientific authors. Becauseof the complexity of the domain they aim to represent, and more specifically thefact that virtually all the scientific actors are connected together, these maps usu-ally contain a large number of links and are really dense and hard to be directlyrepresented.

The said methodology has already been described in the literature in the case ofthe scientograms [26]. But this methodology suffers from some drawbacks. First, thePathfinder algorithm is very slow, avoiding the representation of the maps in an on-line way. Secondly, even if the Kamada-Kawai algorithm is the most used networkdrawing algorithm in this topic [18], it suffers from some aesthetic problems. Infact, this algorithm has no explicit procedure neither to avoid edge crossings, nor tofill properly the full space allocated for the drawing. In the literature, the slownessof the Pathfinder algorithm has already been solved using a fast variant [23], but noalgorithm has yet been proposed to overcome the drawbacks of the visualization ofthe Kamada-Kawai algorithm.

In fact, for the analysis of scientograms, the drawbacks of the Kamada-Kawaialgorithm could prevent an expert from an optimal interpretation of the relationshipstaking place inside the considered scientific domain. For instance, edge crossingscan make a node and its labels overlap, thus avoiding a good reading of the map.Another point is the absence, in the Kamada-Kawai algorithm, of specific spatial

Vmap-Layout, a Layout Algorithm for Drawing Scientograms 3

constraints to avoid the links going back to the center of the map. Spatial artifacts,such as nodes appearing close together even if they are spatially-separated by severallinks, could convey false or misinterpreting information.

In this chapter, we propose a new drawing algorithm to overcome these draw-backs. The structure of the current contribution is as follows. In the second section,we review the existing methodology to design scientograms. In the third section,we describe our proposal. In the fourth section some experiments will be shown.Finally, some concluding remarks are pointed out in the last section.

2 A Methodology to Generate Scientograms

The achievement of a vast scientogram is a recurrent idea in the modern age. In1998, Chen [7, 8] was the first researcher to bring forth the use of PFNETs in ci-tation analysis. This is due to the fact that scientograms are the most appropriatemeans to represent the spatial distribution of research areas, while also affording in-formation on their interactions [25]. Taking the latter as a base, Moya-Anegón et al.[20] proposed a method for the visualization and analysis of vast scientific domainsusing the ISI1-JCR category co-citation information. They represented it as a socialnetwork, simplified that network by means of the Pathfinder algorithm consideringq = n− 1 and r = ∞, and graphically depicted its layout using the Kamada-Kawaialgorithm [14], thus getting a structural model of the scientific research in a vastdomain. Note that r = ∞ and q = n− 1 are the common parameter values whenPathfinder is used for large domains scientogram generation. These values are veryadvantageous for large network pruning [9].

The different method stages are briefly described as follows. The last step is theone replaced by our proposal.

2.1 Category co-citation measure

Co-citation is a widely used and generally accepted technique for obtaining rela-tional information about documents belonging to a domain. Because we strive torepresent and analyze the structure of vast domains, whether they be thematic, geo-graphic or institutional, we fall back on to ISI-JCR co-citation categories [20] as atool for this purpose.

Hence, once the rough information of the ISI-JCR co-citation for the categoriespresent in the domain to be analyzed is obtained, a co-citation measure CM is com-puted for each pair of categories i and j as follows:

CM(i j) = Cc(i j)+Cc(i j)

√

c(i) · c( j)(1)

1 Currently registered as Thomson Scientific.


where Cc is the co-citation frequency and c is the citation frequency.Notice that the aim of this scientogram generation method is that the final sci-

entogram obtained is a tree. Hence, in order to avoid the existence of cycles inthe pruned network, the considered measure of association adds the normalized co-citation (divided by the square root of the product of the frequencies of the co-citeddocuments’ citations [24]) to the rough category co-citation frequency. In this way,the network weights become real numbers, allowing us to create small differencesbetween similar values for the co-citation frequency, thus avoiding the occurrence ofcycles and achieving the optimal prune of each link considering the citing conditionsof each category.

2.2 Network pruning by Pathfinder

Then, the Pathfinder algorithm is applied to the co-citation matrix to prune the net-work. We should take into account the fact that the networks resulting from citation,co-citation, or term co-occurrence analysis are usually very dense, when the cate-gories are used as the unit for each node. Due to this fact, and especially in the caseof vast scientific domains with a high number of entities (categories in our case) inthe network, Pathfinder is parameterized to r = ∞ and q = n−1, in order to obtainan schematic representation of the most outstanding existing information by meansof a network showing just the most salient links. In general, the weights of the linksof the co-citation matrix belong to R and are all different, so the final result of thePathfinder algorithm is a tree. To perform this step, the MST-Pathfinder algorithm,a quick version of the original Pathfinder algorithm based on Minimum SpanningTrees, is used [23].

2.3 Network layout by Kamada-Kawai

Kamada-Kawai algorithm [14] is then used to automatically produce representa-tions of the pruned network resulting from the Pathfinder run on a plane, start-ing from a circular position of the nodes. It generates social networks with aes-thetic criteria such as common edge lengths, forced separation of nodes, building ofbalanced maps, etc. Nevertheless, the satisfaction of some criteria are not directlyimplemented in the Kamada-Kawai algorithm. This is the case of the number ofcrossed links: in fact many links crossings appear making a lot of nodes overlap,and making the reading of the map harder. Another point is the fact that edges cango backwards to the center of the map, putting close two nodes linked by a longpath. This can give a false impression of closeness to the expert due to the spatialdistribution of the nodes. These are two of the main drawbacks we observed whileusing the Kamada-Kawai visualization applied to co-citation networks.


An example of the render of the Kamada-Kawai applied on the co-citation net-work of Europe is shown in figure 1.

Fig. 1 An example of a scientogram corresponding to the Europe scientific domain in 2002

2.4 Advantages and Drawbacks of our Methodology

Since its proposal in 2004, this methodology has been applied to compare the struc-ture of vast scientific domains [19, 26], to the macro- and micro-structural analysisof a specific domain [17, 18], and even to study their evolution through time [27, 28].

Hence, it is actually a very powerful tool due to its summarization capabilityas well as its simplicity to represent the relational information linked through aseries of intelligible sentences, that make easier the comprehension, analysis andinterpretation of a scientific domain. However, the critics that can be made on theKamada-Kawai algorithm about the crossed links make difficult to apply it for thegeneration of scientograms in an automatic way, as a human post-processing is cur-rently needed to avoid the crossings and move the labels in order they can be readclearly. We aim to solve these drawbacks using a new visualization algorithm, as wewill see in the remainder of this chapter.


2.5 The use of other network layout algorithms for social networksdrawing

Apart from the Kamada-Kawai algorithm, an extensive number of graph drawingalgorithms has been already published in the literature [1, 2]. But very few of themhave been devoted to the drawing of social networks due to the high complexity ofthis kind of networks [18].

In [5], the authors have chosen a radial-based network drawing algorithm to rep-resent a collaboration network, and they named it Visone. In this kind of radialdrawing, the nodes are placed in concentric circles, thus highlighting the role ofthe central elements and pushing away the less important elements on the bound-aries. Other studies on the same kind of drawing algorithms for citation networks orco-authorship networks are presented in [6, 4]. Although the obtained representationis nice, the placement of the nodes are too much constrained, thus the length of thelinks can suffer from meaningless growing, making the map harder to understand.

In general, force-directed layout algorithms are studied in the literature to dealwith social networks. The study of Katz and Stafford [15] present the results ob-tained with the Fruchterman-Reingold algorithm compared to the Kamada-Kawaialgorithm to visualize the American Federal Judiciary network. The Fruchterman-Reingold algorithm is also used in [11] for the visualization of the evolution of socialnetworks over time. In general this algorithm gives interesting results as it revealsclusters of nodes. For our application to the co-citation networks, both force-directedlayout algorithms were tested, but the Kamada-Kawai algorithm was preferred dueto its aesthetic behavior [18].

In conclusion, a few different drawing algorithms are studied in the literature,while the need of a comprehensible and aesthetic drawing algorithm is growing associal networks become more and more complex.

3 Overview of the algorithm

This section describes our drawing algorithm. As said, our methodology ensuresthat the result of the Pathfinder algorithm, the network we have to draw, is a tree.Thus, to develop our algorithm, we took as a base the tree visualization algorithmpresented in [21], and extend it to make it applicable on scientograms. The basicversion of the algorithm is first presented, then several variants are discussed for thespecific case of scientogram design.


3.1 Main algorithm

To ease the understanding of our proposal, some preliminary terminology is first in-troduced. In the following, we consider an ordered tree T , in which each node N hasa parent P=PARENT(N), except the root node R=ROOT(T ). CHILDREN(N) is theset of nodes having node N as their parent. ASCENDANT(N) is the chain of nodesfrom node N to the root node R, defined as { N, PARENT(N), PARENT(PARENT(N)),..., R }. SUBTREE(N) is the subtree having node N as its root. SIZE(N) is equalto the number of nodes in SUBTREE(N), including its own root. For instance,SIZE(N) is equal to 1 for a node having no children; 2 for a node having one child;etc. LEVEL(N) is the number of nodes in the set ASCENDANT(N). For instance,LEVEL(N) is equal to 1 for the root node; 2 for any of the children of the root node;etc. DEPTH(N) is the maximum value for LEVEL(M) for any node M in the treeSUBTREE(N). For instance, DEPTH(N) is equal to 1 for a node having no child; 2for a node having any number of children, with none of them having children; etc.By convention, we will also use the notation ROOT(T ) to define the node havingthe lowest level in a subtree T .

The algorithm is named Vmap-Layout due to the kinds of maps it draws, Vi-sual Science Maps, another name for scientograms. It is divided itself in three sub-functions which are called in a sequential way. The first sub-function, AttributeComputation, computes for each node the attributes needed for the remainder ofthe algorithm. The second sub-function, Node Positioning, is a recursive functionaiming to compute the coordinates of each node. The last one, Node Relocation,adjusts the location of the nodes according to some specific criteria, thus improv-ing the final visualization. The different sub-functions are detailed in the followingsub-sections.

3.2 Attribute Computation

Within the first sub-function, we compute several attributes assigned to each node:SIZE(N), LEVEL(N), and DEPTH(N). These attributes will be used later to facil-itate the generation of the coordinates of each node and to improve the runtime ofthe algorithm. The first step is to select a root node, the one that will be printedin the center of the map. It will be used to compute some specific attributes whichcannot be computed without the definition of a root node. The network generatedby the Pathfinder algorithm does not self-contain any root node, thus we have to usean additional technique to select one. There are many ways to select a center in agraph. Many of them are described by Bavelas [3] and Parlebas [22]. The one usedhere, that gives good visual results, is the deliverer criterion: we compute the sumof the distances between any node and all the others, and we take as the root the onehaving the smaller value. Once we have selected the root node R, a number of otherattributes can be computed. Giving R, we can assign to each node N the values cor-responding to SIZE(N), LEVEL(N) and DEPTH(N). As the tree is represented in


memory using lists of children, the time complexity of all these operations is O(n)where n = SIZE(R). The complexity of Attribute Computation is thus O(n). Thesub-function is outlined in Fig. 2.

1. Compute the root node using the deliverer criterion: compute the sum of the distances be-tween a node and all the others, and take as a root the one having the smaller value.

2. Assign to each node N the values given by SIZE(N), LEVEL(N) and DEPTH(N).

Fig. 2 The Attribute Computation sub-function

3.3 Node Positioning

Using the second sub-function, the algorithm fixes the location of each node as apair of 2D coordinates. To do so, the global idea is to fill as much space as possi-ble. The tree is drawn from the root node to the leaves, and the algorithm runs in arecursive way: the root node is drawn in the center of the map and at each iterationthe algorithm draws all the nodes N having the same level L=LEVEL(N). The algo-rithm starts by selecting a region of the empty space in which it can draw the tree(we will call this region initial polygon in the following). Then, it assigns the rootnode to the center of this polygon, it divides the initial polygon into several slices(as many as the number of children in the root node), and it assigns one children ofthe root node to each slice. After the application of this function, the coordinates ofthe center of the polygons are assigned to each node.

There are several ways to design the initial polygon. As the whole tree will lieinside the initial polygon, the later will determine the final shape of the full map.This shape could be a square, a circle or any other n-sided polygon. Fig. 6 showssome possibilities for the initial polygon. The assignation of a center C to a givenpolygon could also be done in several ways. Some techniques are shown in Fig. 8.Lastly, the way of dividing a given polygon into different slices can also been donein several ways, which are detailed in the next sections.

Once the coordinates of the first level of the tree are fixed, the algorithm startsagain, considering each of the slices as a new polygon and the corresponding node Nas the root of a new subtree S=SUBTREE(N). Once no children has been found, thealgorithm stops. The sub-function is outlined in Fig. 4. As we are using a recursivefunction based on the children on a given node, the complexity of Node Positioningis thus O(n).

At the end of this sub-function, all the nodes of the tree have been assigned toa pair of coordinates in the 2D-space. An example of the execution of this sub-function on a tree is shown in Fig. 3.


Fig. 3 An example of the execution of the Node Positioning sub-function

1. Let P, a 2D-space region in which to draw the tree, and T , a tree.2. Choose a central point C in P and assign to this point the root of the tree R=ROOT(T ).3. If CHILDREN(R) is empty, stop.4. Divide P in different slices (sub-polygons), giving as many sub-polygons that the number of

children of R. Let Ri be a child of R, the area of the corresponding sub-polygon Pi should beproportional to SIZE(Ri).

5. For each child Ri of R, run Node Positioning on the region Pi and the tree Ri.

Fig. 4 The Node Positioning sub-function

3.4 Node Relocation

The goal of the third sub-function is only aesthetic. At the end of the application ofthe previous sub-function, some graphical elements, such as the nodes or the textlabels, can overlap. By relocating the nodes, we improve the placement of the over-lapping elements. Here, having the coordinates of the nodes generated previously,the algorithm fixes the final location of each node to avoid as much as possible theseoverlaps. We say that two nodes overlap when they are too close from each other,according to a distance defined by the expert, and we call them problematic nodes.Problematic nodes cause text labels not to be read in a clear way, and reduces ingeneral the readability of the map. The main idea of this function is to apply a noderelocation process in which the problematic nodes are moved according to a repul-sive force depending on the surrounding nodes, like if they were connected withrepulsive springs. To avoid deadlocks in some cases (for instance, when a node islocated exactly between other two nodes and at an equal distance), the problematicnodes are also slightly moved in a random direction, until they met a criterion setby the expert.


The sub-function is outlined in Fig. 5. As the time complexity of the KD-Treepreprocessing is O(n · log(n)) and the time complexity of the KD-Tree search forone node is O(log(n)) [?], the time complexity of Node Relocation is O(n · log(n)).Thus, the complexity of the full algorithm is O(n · log(n)).

1. Apply a KD-Tree technique to compute the distance between all the nodes of T .2. Select only the problematic nodes, i.e. the nodes close enough according to a criterion defined

by the expert.3. For each node of this set, do:

• Apply a repulsive strength δ and move the node along this force.• Move it around its final position using a small random distance in the interval [−σ ,σ ].

4. Execute again the Node Relocation sub-function until a given amount of iterations defined bythe expert has been reached.

Fig. 5 The Node Relocation sub-function

At the end of the third function, the final coordinates of the nodes have beencomputed. During the final drawing of the nodes, additional improvements could bemade in order to improve the aesthetic aspect of the map. For instance, nodes andlabels sizes can be varied depending on their depth in the tree to better highlight thecenter of the map.

3.5 Selecting different initial polygons

During the initialization of the Vmap-Layout algorithm, we have to select the initialpolygon, within which the full tree has to be drawn. This polygon encloses all thelayout and its shape will determine the global shape of the drawing.

Fig. 6 Initial polygons with 4 or 8 sides

In order to improve the general aspect of the final map and to customize theresult for several uses (paper or on-line drawing), several options can be used. Thedefinition of this shape is controlled by an expert parameter, giving the number ofsides the inital polygon should have (see Fig. 6). The larger this value is, the morecircular the shape will be, but the slower will the algorithm run. This is due to the


A

EDCBA

B C

DE

Fig. 7 On the left, the tree to draw. On the right, the initial polygon and the center in black.The polygon is first divided in four slices, because the node A has four children, then we assignthe corresponding nodes to the corresponding sub-polygons. The little circle is the starting pointgiving the direction of the polygon assignment

fact that, as at later stages, the computation of the areas and the angles of a sub-polygon would be more complex. This number of sides does not change in anymanner the further execution of the algorithm but has only an aesthetic aspect.

Once the initial shape is designed, it is used to draw the initial tree, composedof its root and of all its first-level children (see Fig. 7). Any shape surrounding thegraph could be used. For the application to co-citation networks, we opted by a circlebecause the SCImago Research Group2 experts, with whom we collaborate, preferthis shape. Thus, in order to have a good compromise between time and aesthetic,a value of 15 sides seems to be well suited. Larger values than 30 will unneces-sarily increase the runtime and smaller values than 12 would give an impression ofdicontinuity.

3.6 Selecting different ways to compute the central point of apolygon

For each polygon, a central point has to be selected to become the starting pointof the next sub-tree to print (see step 2 in Fig. 4). We have explored at least threedifferent methods to choose the central point C of a polygon P (see Fig. 8). Thefirst method, called ’Center of Mass’, takes for C the center of gravity of P. Thiscenter is defined in any case, but suffers from two problems: it could be outsideof the polygon (this can occur when the polygon is non-convex) and a polygonwith a lot of segments could attract the center far away from the natural centerof the polygon. The second method, called ’Angle-based Central Point’, uses theangle to compute the central point. For a given polygon P, we first select a pointon its border, that we call origin O. This origin O has itself to be defined by somemethods. For instance, the origin could be the center of the parent polygon (the oneused to generate the current polygon), or the left-most point of the polygon. We thendraw a line dividing the angle O in two equal parts. Then we take the middle pointof this line as the center C of the polygon. The third method, called ’Area-based

2 http://www.scimago.es/


Central Point’, applies the same procedure, but by dividing the polygon into twoparts having the same area.

CC

OX

C

O

Xαα Same angle Same area

Fig. 8 Centers positioned with the Center of Mass, the Angle-based Central Point and the Area-based Central Point methods

Our tests have shown that the Area-based Central Point is the best method. How-ever, some problems could occur for some specific shapes of polygons in which it isimpossible to divide a sub-polygon into two areas of equal sizes, pushing the centralpoint C outside the polygon. This can happen when the polygon has internal anglesgreater than π (see Fig. 9), when the chosen initial polygon is non-convex or whenthe structure of the tree is quite uncommon. This is why other methods are provided.

?

O

Same area?

?

O

Same area?

Fig. 9 A problem that can occurs with the Area-based Central Point method: the two areas cannotbe made equals

For the Angle-based Central Point and the Area-based Central Point methods,once the line dividing the polygon in two parts has been determined, we still haveto place the point C over this line. The usual way is to use the middle of the line,as described in the first paragraph of this section. But other values for the measureof the distance OC have been explored. This distance has a direct influence on thelength of the edges and the location of the next sub-polygons, and playing with thisvalue can lead to interesting results on the final drawing. An expert parameter hasbeen set for this measure and is named Cutpoint Value. It is the ratio between thedistance OC and the distance OX (see Fig. 8). With a small value for this parameter,we get maps where the centers are close among them, and with a larger value, weget maps where the centers are more far away among them. Several values for this


parameter have been tried, such as 0.25, 0.5 and 0.6. The best results have beenobtained with values lower or equal to 0.5.

3.7 Selecting different dividing slice methods

C

50%C

25%

25%25% 25%

50%

Fig. 10 The result of the dividing using the Angle-based Dividing (on the left part) and the Area-based Dividing (on the right part) methods

The way to divide a polygon in different slices (see step 4 in Fig. 4) will de-termine the respective areas for the drawing of the next sub-polygons. Small ar-eas should be allocated to small sub-trees whereas larger areas should be allocatedto larger sub-trees. This operation can be achieved by at least two methods (seeFig. 10). With the first method, called Angle-based Dividing, the algorithm definesthe size of the slices in order the angle around the center C is proportional to thesize of each sub-tree Ri. With the second method, called Area-based Dividing, thealgorithm defines the size of the slices in order the area around the center C isproportional to the size of each sub-tree Ri. In many scientograms generated usingreal world data, the second method does not work properly because the non-convexshapes of the polygons make the finding of a percentile using the area an impossibleproblem (see Fig. 9). Therefore, in our application, we always used the Angle-basedDividing method.

O C O C

Fig. 11 On the left, the normal behavior in which all the space is used to compute the size of eachslice. On the right, a modified behavior in which a constraint is applied before computing the sizeof each slice, allowing us to direct the network in a given way

Any use of the two previously described methods needs a measure defined foreach node in order to compute the proportion in percentage allocated to the corre-sponding sub-polygon. The simplest way, called the Sub-size-based Ratio Compu-


(1) Normal behavior

Measure : the ‘sub_size’ attributeNode Measure ProportionB 1/8 12.5%C 5/8 62.5%F 3/4 75%H 1/2 50%

(2) Modified behavior

Measure : the ‘sub_depth’ attributeNode Measure ProportionB 2/2 the value ‘START’C 2/4 0.5 ‘START’ + 0.5 ‘END’F 3/4 0.25 ‘START’ + 0.75 ‘END’H 4/4 the value ‘END’

Tree

A

B C D E

F G

H I

Fig. 12 Different ratio computation methods for dividing the slices: an example of a tree (left); theproportions obtained using the Sub-size-based Ratio Computation method (top); and the propor-tions obtained using the Sub-depth-based Ratio Computation method (bottom)

tation, is to take the size of each node (defined by the SIZE(T ) attribute), i.e. thenumber of nodes in a subtree T , to compute a proportional ratio assigned to thechildren of T . Then, this ratio is used as a percentage to compute the size of all theslices of the corresponding sub-polygons. Nevertheless, this method suffers from alack of customization possibilities by the expert.

Another method, called the Sub-depth-based Ratio Computation, has been ex-plored. It uses the depth of the trees, defined by the DEPTH(T ) attribute, to modifythe proportion allocated to each slice depending on if they are close or far awayfrom the center of the map. The expert has to set two additional parameters, theproportion given for the allocation of the slice of the lowest level, corresponding tothe initial root of the tree (this value has been named ’START’), and the proportiongiven for the allocation of the slice of the deepest level, corresponding to a givenleaf of the tree (this value has been named ’END’). Because only these two values,START and END, have to be specified by the expert, the remaining values used tofix the proportion of the intermediate levels are computed using a linear regression.Using another point of view, the START value fixes the behavior of the nodes closeto the center of the map (or the backbone), which are the most important ones, andthe END value fixes the behavior of the minor nodes shown in the periphery. Theseparameters are thus useful for our application of co-citation networks. We have ob-tained the best results using 0.5 and 0.25 for the respective values of START andEND.

The behavior of the Sub-depth-based Ratio Computation method is very simple.It allows us to constrain the angle of the links to go only forward when we areclose to the center of the map (see Fig. 11). In fact, when drawing scientograms,having edges going mainly forward gives a better representation as nodes locatedfar away in terms of number of edges are spatially dissociated. This is why we


selected the Sub-depth-based Ratio Computation method as the default one for ourexperimentations.

To show how the proportion of the slices are computed using the Sub-size-basedRatio Computation and the Sub-depth-based Ratio Computation methods, an exam-ple is presented in Fig. 12 using a small tree. For some selected nodes, the valuesare computed for both methods. The proportion is always computed as a ratio be-tween two numbers, the current attribute of the node (respectively the SIZE and theDEPTH) and the maximum value for this attribute (so, the maximum size of the cur-rent sub-tree or the maximum depth if the second measure is considered). Note thatthe ratio computation method is totally independent from the method of dividingthese slices, i.e. the ratio can be used independently with the Area-based Dividingor the Angle-based Dividing methods.

3.8 Details on the Node Relocation function

Once the coordinates of the nodes have been found by the Node Positioning sub-function (see Fig. 4), a node relocation stage occurs in order to improve the locationof the overlapping nodes. This stage is done by the Node Relocation sub-function(see Fig. 5).

The goal of this sub-function is to identify the nodes which are too close, ac-cording to an expert criterion, and to move them randomly in order to avoid theoverlapping of the nodes. The process is iterated several times until a perfect con-figuration is found by the algorithm. Because of the cost of the computation of thedistance between nodes, and since this process has to be iterated, we use a KD-Treetechnique to compute these distances. A KD-Tree allows the computation of thedistance between a set of nodes in order we can quickly know which set of nodesare closer to any given node3.

0.2 0.17

0.07

0.2 0.17

0.07

Fig. 13 An example of the modification of the coordinates of a node after applying the NodeRelocation function

3 The library we have used for this process is called the ANN Library [16]. The advantage ofthis library is that an approximate distance computation is used in order to speed up the process,provided the fact that knowing the exact values of the distances is not important, which is the casein our application.


The Node Relocation sub-function works as follows. A parameter named ra-dius is defined by the expert to specify the minimum allowed distance between twonodes. Only the coordinates of any node having a smaller or equal distance to thisradius will be modified by the algorithm, while the coordinates of the nodes locatedat a greater distance will not be changed. Two additional parameters are defined, thespring-strength δ giving the strength of the movements during the relocation of thenodes and the random-strength σ giving the quantity of randomness applied to thenodes that have to be relocated.

From each node N of the set defined by the radius parameter, we apply a force de-fined as the sum of all the repulsive forces generated by the nodes close to N, multi-plied by the value defined by the spring-strength δ parameter (a repulsive strength),and add a random value chosen into the interval [−σ ,σ ] to it. 13 shows how therepulsive forces generated by all the surrounding nodes apply on a given node, andhow this node is moved. This is done until a given number of iterations have beencompleted. A higher value for this parameter can be used to establish the conver-gence of the coordinates of the nodes, but at the cost of slowing down the process.We have obtained good and fast results with a value of 100 iterations.

The spring-strength δ parameter is used to define the step size of movementapplied to the node. A small value moves the nodes slowly through the iterationsof the algorithm, while a bigger value allows sudden changes of the coordinatesof the nodes. A value of 0.10 was used in our experiments. The random-strengthdefines the quantity of randomness applied to the location of the node at the end ofeach iteration. A value of zero disables any randomness during the movement of thenodes. A value of 0.05 was used.

4 Experiments

In this section, we will show the results obtained on some scientograms. The data aredirectly extracted from a database of co-citation measures for Europe, generated in2002. Some specific criteria are set in order to select a subset of the whole databaserestricted to four world regions, Europe, USA, Spain and Cuba. The resulting fileencodes a fully connected network, with labeled nodes and weighted links, ready tobe pruned. Thus, the first step is to use the MST-Pathfinder algorithm to prune thesenetworks in order to get trees. The computing time for this step is roughly 9 ms onan Intel dual-core Pentium 3.2 GHz with 2 GB of memory.

The next step is to print the maps using the Vmap-Layout algorithm. The algo-rithm has been written in C++, and compiled on Linux with the GNU GCC com-piler with the -O3 option. The computing time using the Vmap-Layout algorithmis roughly 71 ms. The main parameters used are as follows. The initial polygon has15 sides. The central point has been computed using the Angle-based Central Pointmethod. The Cutpoint Value has been set to 0.5. The slices have been divided usingthe Angle-based dividing method. Finally, the Sub-depth-based Ratio Computationhas been used to position the central point in the polygon.


A comparison has been performed using the Kamada-Kawai algorithm. For thispurpose, we have used the GraphViz library. GraphViz is an open source networkdrawing software, freely provided by AT&T Labs, and available at: http://www.graphviz.org/. It integrates the Kamada-Kawai algorithm in the form of the neatoutility. This utility exports in diverse graphical formats a description of a networkdone with a proprietary language, the DOT language [13]. Thus the second stepwas to convert the previous network in the format accepted by this library. Thecomputing time using the Kamada-Kawai algorithm is 0.6 ms.

The last step is to generate the graphical output from the DOT description usingneato. Actually, as these maps are designed for on-line consultation, the ScalableVector Graphics (SVG) format was chosen. The time to generate the SVG image is1300 ms. The following command was used to generate this map, once the libraryis installed:

dot -Kneato -Tsvg -o Europe.svg Europe.dot

The final results, for the Vmap-Layout and the Kamada-Kawai algorithms areshown in Fig. 14 and Fig. 15 for the Europe; in Fig. 16 and Fig. 17 for the USA; inFig. 18 and Fig. 19 for Spain; and in Fig. 16 and Fig. 17 for the USA; in Fig. 20 andFig. 21 for Cuba.

Several remarks can be made from these pictures. First, we have to notice thatthe Vmap-Layout algorithm avoids the edge crossings as expected, as each sub-treeis drawn in its own sub-space. Secondly, the nodes connected to the central node areproperly spaced, and aligned on its own circle, allowing an expert to read properlythe labels. In the case of the Kamada-Kawai maps, the reading of the top-level labelsis not so clear. Finally, all the space available in the figure is properly filled with theVmap-Layout, giving more space to the larger sub-trees.

5 Conclusion

The Vmap-Layout algorithm is an effective and a fast technique for the represen-tation of co-citation networks. Our algorithm can print real world networks in anaesthetic way, highlighting the backbone and pushing the less important links tothe boundaries. Several variants have been described, allowing an expert to tune therepresentation depending on his needs.

We are currently investigating other improvements of this algorithm. One optionis to allow it to use extra space over the polygons in order to reduce the white spacebetween the edges. Another option is the use of different techniques for the noderelocation, for instance based on the simulated annealing metaheuristic, to find abetter positioning of the nodes. We are also planning some experiments on otherkinds of real data sets, including larger networks.


ENERGY & FUELS

GEOSCIENCES, INTERDISCIPLINARY

ENGINEERING, PETROLEUM

404.243195

GASTROENTEROLOGY & HEPATOLOGY

RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING

MATHEMATICS

MEDICINE, GENERAL & INTERNAL

2978.083008

EDUCATION, SCIENTIFIC DISCIPLINES

MEDICAL INFORMATICS

ENTOMOLOGY

CHEMISTRY, MULTIDISCIPLINARY

CONSTRUCTION & BUILDING TECHNOLOGY

MATERIALS SCIENCE, MULTIDISCIPLINARY

416.067993

COMPUTER SCIENCE, THEORY & METHODS

COMPUTER SCIENCE, INFORMATION SYSTEMS

COMPUTER SCIENCE, SOFTWARE, GRAPHICS, PROGRAMMING

2270.375732

2016.345215

MATHEMATICS, APPLIED

2931.215088

ACOUSTICS 733.095215

CARDIAC & CARDIOVASCULAR SYSTEMS

6216.125977

RESPIRATORY SYSTEM

3517.178955

AGRICULTURE, DAIRY & ANIMAL SCIENCE

AGRICULTURE

AGRICULTURE, SOIL SCIENCE

822.185486

NUTRITION & DIETETICS

FOOD SCIENCE & TECHNOLOGY

889.135681

ANESTHESIOLOGY

ANATOMY & MORPHOLOGY

ENGINEERING, AEROSPACE

ASTRONOMY & ASTROPHYSICS

3893.140381

BIOCHEMISTRY & MOLECULAR BIOLOGY

7370.062500

643.024963

6269.059082

2257.051270

PLANT SCIENCES

2103.184570

5788.081055

ZOOLOGY

1878.042969

BIOLOGY

8780.141602

BIOTECHNOLOGY & APPLIED MICROBIOLOGY

10305.148438

SURGERY

4163.087891

CRYSTALLOGRAPHY

2948.111572BIOCHEMICAL RESEARCH METHODS

14153.200195

CELL BIOLOGY

940.065918

33247.257812

DERMATOLOGY & VENEREAL DISEASES

1094.027222

ENDOCRINOLOGY & METABOLISM

7990.095215

HEMATOLOGY

ENVIRONMENTAL SCIENCES

WATER RESOURCES

2537.215576

MARINE & FRESHWATER BIOLOGY

METALLURGY & METALLURGICAL ENGINEERING3546.242920

MECHANICS

MEDICINE, RESEARCH & EXPERIMENTAL

10810.149414

NEUROSCIENCES

8341.075195

CLINICAL NEUROLOGY

1289.083374

8645.186523

PATHOLOGY

3683.073730

OBSTETRICS & GYNECOLOGY

1789.063843

DENTISTRY, ORAL SURGERY & MEDICINE

687.051514

ECOLOGY

2198.156250

ONCOLOGY

2158.068848

9501.095703

OPHTHALMOLOGY

787.035583

ORTHOPEDICS

2140.133057

OTORHINOLARYNGOLOGY

800.072083

PEDIATRICS

2256.078369

PHARMACOLOGY & PHARMACY

11606.125977

PHYSICS, MULTIDISCIPLINARY

326.027374

PHYSIOLOGY

7858.105957

POLYMER SCIENCE

PHYSICS, APPLIED

ENGINEERING, CHEMICAL

997.135376

PSYCHIATRY

4590.172852

TROPICAL MEDICINE

PARASITOLOGY

752.028564

VETERINARY SCIENCES

VIROLOGY

SUBSTANCE ABUSE

509.093445

ENGINEERING, MECHANICAL

1603.214722

MICROBIOLOGY

6804.089844

STATISTICS & PROBABILITY

739.176270

PHYSICS, NUCLEAR

7593.098145

OPTICS

PHYSICS, ATOMIC, MOLECULAR & CHEMICAL

8080.104004

6182.176758

BIOPHYSICS

14844.210938

CHEMISTRY, ORGANIC

7423.182617

CHEMISTRY, ANALYTICAL

10047.352539

MEDICAL LABORATORY TECHNOLOGY

2416.076660

CHEMISTRY, PHYSICAL

8601.168945

2169.082031

2946.118652

7429.155762

MATERIALS SCIENCE, COMPOSITES

295.045532

REPRODUCTIVE BIOLOGY

1844.215942

GENETICS & HEREDITY

17754.173828

IMMUNOLOGY

9931.100586

1376.0609132465.115479

ENGINEERING, ELECTRICAL & ELECTRONIC

3919.147217

CHEMISTRY, INORGANIC & NUCLEAR

5457.155273

PHYSICS, CONDENSED MATTER

9546.202148

11635.130859

10358.213867

AUTOMATION & CONTROL SYSTEMS

872.126587

METEOROLOGY & ATMOSPHERIC SCIENCES

4577.249512489.101440

2374.132812

BEHAVIORAL SCIENCES

2987.145752

TOXICOLOGY

1968.127563

3650.163086

GERIATRICS & GERONTOLOGY

795.033997

ENGINEERING

775.115601

AGRICULTURAL ECONOMICS & POLICY

FORESTRY

723.078979

HISTORY & PHILOSOPHY OF SCIENCE

COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

2020.289551

1722.135986

ENGINEERING, MANUFACTURING

INFECTIOUS DISEASES

5258.192871

RHEUMATOLOGY

1427.061646

UROLOGY & NEPHROLOGY

1941.063354

TELECOMMUNICATIONS

1391.198730

PALEONTOLOGY

927.119934

ALLERGY

1704.125610

BIOLOGY, MISCELLANEOUS

2812.179443

4528.163574

MATERIALS SCIENCE, CERAMICS

1500.132324

PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH

4502.128418

901.163391EMERGENCY MEDICINE & CRITICAL CARE

335.061829

MEDICINE, LEGAL

279.070160

ANTHROPOLOGY

300.067505

PERIPHERAL VASCULAR DISEASE

9051.286133

8727.282227

REHABILITATION

SPORT SCIENCES

1581.129272

552.169922

INSTRUMENTS & INSTRUMENTATION

GEOCHEMISTRY & GEOPHYSICS

5279.257812

MINERALOGY

1312.146606

ENGINEERING, ENVIRONMENTAL

2897.284424

COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

1116.270386

DEVELOPMENTAL BIOLOGY

5795.118164

ANDROLOGY

175.109390

ENGINEERING, BIOMEDICAL

749.058228

OCEANOGRAPHY

4457.254395PSYCHOLOGY

2726.181396

NUCLEAR SCIENCE & TECHNOLOGY

3898.339600

CHEMISTRY, APPLIED

1833.209961

1896.103271

PHYSICS, FLUIDS & PLASMAS

1970.188599

INFORMATION SCIENCE & LIBRARY SCIENCE

269.118195

PHYSICS, PARTICLES & FIELDS

8002.080078

2806.091553

CHEMISTRY, MEDICINAL 4039.201904

MATERIALS SCIENCE, PAPER & WOOD

246.126129

ERGONOMICS

SPECTROSCOPY

3221.250000

OPERATIONS RESEARCH & MANAGEMENT SCIENCE

680.103088

ENGINEERING, MARINE

THERMODYNAMICS

757.121826

MATERIALS SCIENCE, COATINGS & FILMS

1799.145508

FISHERIES

1468.228394

LIMNOLOGY

1123.138184

MATHEMATICS, MISCELLANEOUS

2883.399414

1881.202515

GEOGRAPHY

756.097961

ORNITHOLOGY

430.091888

MATERIALS SCIENCE, BIOMATERIALS

1246.283691

GEOLOGY

1487.172729

COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

HORTICULTURE

1092.141479

COMPUTER SCIENCE, CYBERNETICS

257.038727

TRANSPLANTATION

2117.127197

PSYCHOLOGY, EXPERIMENTAL

2037.251343

PSYCHOLOGY, MATHEMATICAL

402.206116

MATERIALS SCIENCE, CHARACTERIZATION & TESTING

170.038086

ENGINEERING, CIVIL

801.179443

37.073483

MINING & MINERAL PROCESSING

506.077484

PHYSICS, MATHEMATICAL

2174.133789

7287.155762

2722.198975

3087.227295

ELECTROCHEMISTRY

1287.095093

PSYCHOLOGY, DEVELOPMENTAL606.088867

EDUCATION & EDUCATIONAL RESEARCH

ENGINEERING, INDUSTRIAL

401.284729

237.265121

422.203857

MYCOLOGY

597.093872

PSYCHOLOGY, EDUCATIONAL

306.087189

172.132004

ENVIRONMENTAL STUDIES

432.187653

SOCIAL SCIENCES, BIOMEDICAL

691.161072

PSYCHOLOGY, BIOLOGICAL

927.280762

SOCIOLOGY

LAW

MICROSCOPY

354.022858

REMOTE SENSING

462.086182

TRANSPORTATION

54.027103

PSYCHOLOGY, CLINICAL

1902.190308

IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY

471.344452

MATERIALS SCIENCE, TEXTILES

154.081665ECONOMICS

138.095901

305.064362

108.038307

SOCIAL SCIENCES, MATHEMATICAL METHODS

1432.350098

1396.255005

BUSINESS

MANAGEMENT

490.142426

886.265320

URBAN STUDIES

341.279449

SOCIAL SCIENCES, INTERDISCIPLINARY

236.102661

PLANNING & DEVELOPMENT

495.131836

BUSINESS, FINANCE

723.185547

SOCIAL ISSUES

71.096703

PUBLIC ADMINISTRATION

SOCIAL WORK

107.042625

PSYCHOLOGY, SOCIAL

729.138855

NURSING

398.077484

WOMEN’S STUDIES

83.034630

AREA STUDIES

84.043175

POLITICAL SCIENCE

279.070496

108.137115

CRIMINOLOGY & PENOLOGY

87.031700

INTERNATIONAL RELATIONS

221.189407

EDUCATION, SPECIAL

144.195236

ARCHAEOLOGY

159.167358

HISTORY

FAMILY STUDIES

126.080658

HISTORY OF SOCIAL SCIENCES

97.051498

89.124954

PSYCHOLOGY, PSYCHOANALYSIS

189.062943

LANGUAGE & LINGUISTICS

PSYCHOLOGY, APPLIED

544.142273

HEALTH POLICY & SERVICES

PHILOSOPHY

88.107742

ETHNIC STUDIES

52.125092INDUSTRIAL RELATIONS & LABOR

169.087997

COMMUNICATION

76.090752

DEMOGRAPHY

78.087578

ENGINEERING, GEOLOGICAL

404.089844

HEALTH CARE SCIENCES & SERVICES

1439.084717

55.033871

1092.413330

LITERATURE, ROMANCE

31.115152

THEATER

LITERARY REVIEWS

LITERATURE, SLAVIC

7.079720

ENGINEERING, OCEAN

208.067642

MUSIC

41.024891

LITERATURE

78.084091

88.164314

6.032001

11.038407

POETRY

7.047451

LITERATURE, AMERICAN

2.022628

ARTS & HUMANITIES, GENERAL

56.065639

ARCHITECTURE

7.042204

ART

48.097767

RELIGION

75.091682

Fig. 14 The scientogram of Europe in 2002, drawn with the Kamada-Kawai algorithm

References

1. Battista, G.D., Eades, P., Tamassia, R., Tollis, I.: Algorithms for drawing graphs: An annotedbibliography. Computational Geometry: Theory and Applications 4(5), 235–282 (1994)

2. Battista, G.D., Eades, P., Tamassia, R., Tollis, I.: Graph Drawing. Prentice Hall, Upper SaddleRiver, NJ (1999)

3. Bavelas, A.: Réseaux de communications au sein de groupes placés dans des conditions ex-périmentales de travail, Les sciences de la politique aux États- Unis. Armand Colin, Paris(1951)

4. Brandes, U., Erlebach, T.: Network Analysis: Methodological Foundations. Springer, Berlin(2005). Vol. 3418 of Lecture Notes in Computer Science

5. Brandes, U., Kenis, P., Wagner, D.: Communicating centrality in policy network drawings.IEEE Transactions on Visualization and Computer Graphics 9(2), 241–253 (2003)

6. Brandes, U., Wagner, D.: Graph Drawing Software, chap. Visone–Analysis and Visualizationof Social Networks, pp. 321–340. Berlin (2003)

7. Chen, C.: Bridging the gap: the use of pathfinder networks in visual navigation. Journal ofVisual Languages and Computing 9, 267–286 (1998)


29 BIOCHEMISTRY&

MOLECULARBIOLOGY

6 MEDICINE,GENERAL

&INTERNAL

9 ENTOMOLOGY

10 CHEMISTRY,MULTIDISCIPLINARY

23 NUTRITION&

DIETETICS

30 PLANTSCIENCES

31 ZOOLOGY

32 BIOLOGY

33 BIOTECHNOLOGY&

APPLIEDMICROBIOLOGY

36 BIOCHEMICALRESEARCHMETHODS

37 CELLBIOLOGY

38 DERMATOLOGY&

VENEREALDISEASES

39 ENDOCRINOLOGY&

METABOLISM46 MEDICINE,

RESEARCH&

EXPERIMENTAL

47 NEUROSCIENCES

49 PATHOLOGY

53 ONCOLOGY

58 PHARMACOLOGY&

PHARMACY

60 PHYSIOLOGY

66 PARASITOLOGY71 MICROBIOLOGY76 BIOPHYSICS

79 MEDICALLABORATORYTECHNOLOGY

83 GENETICS&

HEREDITY

84 IMMUNOLOGY

92 GERIATRICS&

GERONTOLOGY

119 DEVELOPMENTALBIOLOGY

165 MICROSCOPY

3 GASTROENTEROLOGY&

HEPATOLOGY

18 CARDIAC&

CARDIOVASCULARSYSTEMS

34 SURGERY

50 OBSTETRICS&

GYNECOLOGY

57 PEDIATRICS

100 RHEUMATOLOGY

101 UROLOGY&

NEPHROLOGY

107 PUBLIC,ENVIRONMENTAL

&OCCUPATIONAL

HEALTH

204 HEALTHCARE

SCIENCES&

SERVICES

19 RESPIRATORYSYSTEM

111 PERIPHERALVASCULAR

DISEASE

40 HEMATOLOGY

51 DENTISTRY,ORAL

SURGERY&

MEDICINE55 ORTHOPEDICS

56 OTORHINOLARYNGOLOGY

108 EMERGENCYMEDICINE

&CRITICAL

CARE

82 REPRODUCTIVEBIOLOGY

120 ANDROLOGY

65 TROPICALMEDICINE

161 SOCIALSCIENCES,

BIOMEDICAL

167 TRANSPORTATION

181 SOCIALWORK

183 NURSING

184 WOMEN’SSTUDIES

96 HISTORY&

PHILOSOPHYOF

SCIENCE

197 HEALTHPOLICY

&SERVICES

198 PHILOSOPHY

35 CRYSTALLOGRAPHY

77 CHEMISTRY,ORGANIC

80 CHEMISTRY,PHYSICAL

86 CHEMISTRY,INORGANIC

&NUCLEAR

61 POLYMERSCIENCE

63 ENGINEERING,CHEMICAL

75 PHYSICS,ATOMIC,

MOLECULAR&

CHEMICAL

125 CHEMISTRY,APPLIED

0 ENERGY&

FUELS

135 THERMODYNAMICS2 ENGINEERING,

PETROLEUM

59 PHYSICS,MULTIDISCIPLINARY

74 OPTICS

7 EDUCATION,SCIENTIFIC

DISCIPLINES73 PHYSICS,NUCLEAR

87 PHYSICS,CONDENSED

MATTER

128 PHYSICS,PARTICLES

&FIELDS

153 PHYSICS,MATHEMATICAL

12 MATERIALSSCIENCE,

MULTIDISCIPLINARY

62 PHYSICS,APPLIED

11 CONSTRUCTION&

BUILDINGTECHNOLOGY

44 METALLURGY&

METALLURGICALENGINEERING


COMPOSITES


CERAMICS150 MATERIALSSCIENCE,

CHARACTERIZATION&

TESTING

152 MINING&

MINERALPROCESSING

85 ENGINEERING,ELECTRICAL

&ELECTRONIC


COATINGS&

FILMS

88 AUTOMATION&

CONTROLSYSTEMS

97 COMPUTERSCIENCE,

ARTIFICIALINTELLIGENCE

102 TELECOMMUNICATIONS

13 COMPUTERSCIENCE,THEORY

&METHODS

15 COMPUTERSCIENCE,

SOFTWARE,GRAPHICS,

PROGRAMMING

118 COMPUTERSCIENCE,

HARDWARE&

ARCHITECTURE

14 COMPUTERSCIENCE,

INFORMATIONSYSTEMS

127 INFORMATIONSCIENCE

&LIBRARYSCIENCE

124 NUCLEARSCIENCE

&TECHNOLOGY

114 INSTRUMENTS&

INSTRUMENTATION

132 SPECTROSCOPY

16 MATHEMATICS,APPLIED

126 PHYSICS,FLUIDS

&PLASMAS 144 COMPUTER

SCIENCE,INTERDISCIPLINARY

APPLICATIONS

5 MATHEMATICS

93 ENGINEERING

133 OPERATIONSRESEARCH

&MANAGEMENT

SCIENCE

157 ENGINEERING,INDUSTRIAL

174 MANAGEMENT

98 ENGINEERING,MANUFACTURING

131 ERGONOMICS

173 BUSINESS

176 SOCIALSCIENCES,

INTERDISCIPLINARY

179 SOCIALISSUES

201 COMMUNICATION

45 MECHANICS

70 ENGINEERING,MECHANICAL

210 MUSIC

24 FOODSCIENCE

&TECHNOLOGY

170 MATERIALSSCIENCE,TEXTILES

20 AGRICULTURE,DAIRY

&ANIMALSCIENCE

21 AGRICULTURE

95 FORESTRY

145 HORTICULTURE

22 AGRICULTURE,SOIL

SCIENCE


PAPER&

WOOD

78 CHEMISTRY,ANALYTICAL

154 ELECTROCHEMISTRY

26 ANATOMY&

MORPHOLOGY

48 CLINICALNEUROLOGY

54 OPHTHALMOLOGY

90 BEHAVIORALSCIENCES


CYBERNETICS

25 ANESTHESIOLOGY

64 PSYCHIATRY

69 SUBSTANCEABUSE

123 PSYCHOLOGY

155 PSYCHOLOGY,DEVELOPMENTAL

168 PSYCHOLOGY,CLINICAL

187 CRIMINOLOGY&

PENOLOGY

194 PSYCHOLOGY,PSYCHOANALYSIS

148 PSYCHOLOGY,EXPERIMENTAL

159 PSYCHOLOGY,EDUCATIONAL

182 PSYCHOLOGY,SOCIAL

196 PSYCHOLOGY,APPLIED

156 EDUCATION&

EDUCATIONALRESEARCH

192 FAMILYSTUDIES

162 PSYCHOLOGY,BIOLOGICAL

109 MEDICINE,LEGAL

4 RADIOLOGY,NUCLEARMEDICINE

&MEDICALIMAGING

17 ACOUSTICS

91 TOXICOLOGY

129 CHEMISTRY,MEDICINAL

41 ENVIRONMENTALSCIENCES

42 WATERRESOURCES

89 METEOROLOGY&

ATMOSPHERICSCIENCES

117 ENGINEERING,ENVIRONMENTAL

138 LIMNOLOGY

151 ENGINEERING,CIVIL

134 ENGINEERING,MARINE

1 GEOSCIENCES,INTERDISCIPLINARY

27 ENGINEERING,AEROSPACE

209 ENGINEERING,OCEAN

28 ASTRONOMY&

ASTROPHYSICS

103 PALEONTOLOGY

115 GEOCHEMISTRY&

GEOPHYSICS

122 OCEANOGRAPHY

140 GEOGRAPHY

143 GEOLOGY

203 ENGINEERING,GEOLOGICAL

116 MINERALOGY

166 REMOTESENSING

169 IMAGINGSCIENCE

&PHOTOGRAPHICTECHNOLOGY

160 ENVIRONMENTALSTUDIES

175 URBANSTUDIES

113 SPORTSCIENCES

112 REHABILITATION

189 EDUCATION,SPECIAL

158 MYCOLOGY

121 ENGINEERING,BIOMEDICAL


BIOMATERIALS

105 BIOLOGY,MISCELLANEOUS

52 ECOLOGY

110 ANTHROPOLOGY

139 MATHEMATICS,MISCELLANEOUS

43 MARINE&

FRESHWATERBIOLOGY

141 ORNITHOLOGY

137 FISHERIES

190 ARCHAEOLOGY

215 ARCHITECTURE

216 ART

72 STATISTICS&

PROBABILITY

149 PSYCHOLOGY,MATHEMATICAL

172 SOCIALSCIENCES,

MATHEMATICALMETHODS

8 MEDICALINFORMATICS

171 ECONOMICS

94 AGRICULTURALECONOMICS

&POLICY

163 SOCIOLOGY

164 LAW

177 PLANNING&

DEVELOPMENT

178 BUSINESS,FINANCE

185 AREASTUDIES

186 POLITICALSCIENCE

193 HISTORYOF

SOCIALSCIENCES

200 INDUSTRIALRELATIONS

&LABOR

199 ETHNICSTUDIES

202 DEMOGRAPHY

180 PUBLICADMINISTRATION

188 INTERNATIONALRELATIONS

191 HISTORY

211 LITERATURE 214 ARTS&

HUMANITIES,GENERAL

217 RELIGION

195 LANGUAGE&

LINGUISTICS

206 THEATER

207 LITERARYREVIEWS

212 POETRY

213 LITERATURE,AMERICAN

205 LITERATURE,ROMANCE

208 LITERATURE,SLAVIC

67 VETERINARYSCIENCES

68 VIROLOGY

99 INFECTIOUSDISEASES

104 ALLERGY147 TRANSPLANTATION

Fig. 15 The scientogram of Europe in 2002, drawn with the Vmap-Layout algorithm

8. Chen, C.: Generalised similarity analysis and pathfinder network scaling. Interacting withcomputers 10, 107–128 (1998)

9. Chen, C.: Information Visualization: Beyond the Horizon. Springer, Berlin, Germany (2004)10. Dearholt, D., Schvaneveldt, R.: Properties of pathfinder networks. In: Pathfinder associative

networks: Studies in knowledge organization, pp. 1–30. Ablex Publishing Corporation (1990)11. Dynes, S.B.C., Gloor, P.A., Laubacher, R., Zhao, Y., Dynes, S.: Temporal visualization and

analysis of social networks. In: North American Association for Computational Social andOrganizational Science Conference (NAACSOS), Pittsburgh (2004)

12. Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Software- Practice and Experience 21(11), 1129–1164 (1991)

13. Gansner, E.R., North, S.C.: An open graph visualization system and its applications to soft-ware engineering. Software — Practice and Experience 30(11), 1203–1233 (2000)

14. Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. InformationProcessing Letters 31(1), 7–15 (1989)

15. Katz, D.M., Stafford, D.K.: Hustle and flow: A social network analysis of the american federaljudiciary. In: Annual Meeting of the The Law and Society Association (2008)


ENERGY & FUELS



381.291870



MATHEMATICS



MEDICAL INFORMATICS

ENTOMOLOGY







1291.346436

1058.258911


1458.178467

ACOUSTICS

435.072968


RESPIRATORY SYSTEM

2998.182617


AGRICULTURE




492.144257

ANESTHESIOLOGY




3347.176514


2044.041870

6516.059082

562.021118

4899.057617PLANT SCIENCES

1272.185059

3112.059326

ZOOLOGY

BIOLOGY

7906.141602


908.094238

8870.145508

SURGERY

3671.088379

CRYSTALLOGRAPHY

1400.045166

BIOCHEMICAL RESEARCH METHODS

10589.182617

CELL BIOLOGY

802.060303

33309.253906

DERMATOLOGY & VENEREAL DISEASES866.026489


1689.114990

7264.099121

HEMATOLOGY

5935.083496


1691.107544

497.080902

WATER RESOURCES

1668.187378


METALLURGY & METALLURGICAL ENGINEERING

1731.236694

MECHANICS 1371.120605


10535.151367

NEUROSCIENCES

8589.080078

1754.074951

CLINICAL NEUROLOGY

1066.094360

6873.169922

PATHOLOGY

3366.076172


1595.070923


480.043823

ECOLOGY

1377.143311

ONCOLOGY

1897.069458

9941.105469OPHTHALMOLOGY

850.023804

ORTHOPEDICS

2063.134033

OTORHINOLARYNGOLOGY

786.087097

PEDIATRICS

2577.090820PHARMACOLOGY & PHARMACY

9297.117188


PHYSIOLOGY

8442.111328

POLYMER SCIENCE

1207.066772

PHYSICS, APPLIED


578.136475

PSYCHIATRY

3945.103516

TROPICAL MEDICINE

PARASITOLOGY

503.026276

VETERINARY SCIENCES

VIROLOGY

2512.060791

SUBSTANCE ABUSE

1015.112793


1173.200684

MICROBIOLOGY

4773.082031


1791.202026

PHYSICS, NUCLEAR

3180.095703OPTICS


4188.106445

3007.161377

BIOPHYSICS 12196.196289

CHEMISTRY, ORGANIC

4072.166260


6222.357422


1647.168091

CHEMISTRY, PHYSICAL

4869.166016

1237.100586

3984.159668


176.050705

REPRODUCTIVE BIOLOGY

1071.195557

GENETICS & HEREDITY

17801.181641

IMMUNOLOGY8994.097656

1045.058838


1133.135376

2777.148193


2470.136719


4178.187988

5325.132812

4959.201172


589.120911


3915.256836

278.058563

BEHAVIORAL SCIENCES

2904.143311

TOXICOLOGY

1618.129517

3329.181396


799.037659

ENGINEERING

478.109131


FORESTRY

538.098328



1129.141968


INFECTIOUS DISEASES

4927.209473RHEUMATOLOGY

907.052673


1886.041016

TELECOMMUNICATIONS

1384.213501

PALEONTOLOGY

450.093018

ALLERGY

961.105286


3884.2731932191.167236


676.128174


5273.151855

563.107788

535.123901

EMERGENCY MEDICINE & CRITICAL CARE

524.050354

MEDICINE, LEGAL

226.026749

ANTHROPOLOGY

366.067291


7975.295410

7260.279785

REHABILITATION SPORT SCIENCES

1528.112549

683.165283



4101.267090

MINERALOGY

636.117859


2121.264160


987.151367


7388.138184

ANDROLOGY

107.013832


672.068237

OCEANOGRAPHY

3626.272705

PSYCHOLOGY

3450.176514


1157.261353

CHEMISTRY, APPLIED

811.075562


1408.220337


431.168121


3553.078613

CHEMISTRY, MEDICINAL 2739.178711MATERIALS SCIENCE, PAPER & WOOD

161.150925

ERGONOMICS

166.062424

SPECTROSCOPY

1465.106567

1203.210205


ENGINEERING, MARINE

THERMODYNAMICS

535.165710


866.122192

FISHERIES

960.214600

LIMNOLOGY

1088.154419


3338.451904

2126.241699

GEOGRAPHY

433.078064

ORNITHOLOGY

319.084808

MATERIALS SCIENCE, BIOMATERIALS873.290405

GEOLOGY

821.145325


HORTICULTURE

583.124573


146.029327

TRANSPLANTATION

1754.123535


2067.219971


610.232727


103.039246

ENGINEERING, CIVIL

269.201599

682.200317

40.104919


296.084137


3075.147461

1508.221069

ELECTROCHEMISTRY

658.269287

PSYCHOLOGY, DEVELOPMENTAL

1270.136475


477.063904

ENGINEERING, INDUSTRIAL 312.253693443.230255

MYCOLOGY

459.036255


787.193787



638.127991


975.292419

SOCIOLOGY

LAW

MICROSCOPY

270.022766

REMOTE SENSING

487.097137

TRANSPORTATION

92.043037


3031.197266


510.338013


71.078392

ECONOMICS

244.116898

403.085114

478.040405

SOCIAL SCIENCES, MATHEMATICAL METHODS

1742.391479

1564.252319

BUSINESS

560.070068

MANAGEMENT 619.161804

1430.269043

URBAN STUDIES


536.087463


447.115662

246.220993

BUSINESS, FINANCE

1201.194824

SOCIAL ISSUES

189.100967


136.046341

SOCIAL WORK

PSYCHOLOGY, SOCIAL

1657.175537

NURSING

683.104736

WOMEN’S STUDIES

272.059265

AREA STUDIES

POLITICAL SCIENCE

436.068085

148.105515



444.180359

EDUCATION, SPECIAL

391.262451

ARCHAEOLOGY

227.153427

HISTORY

FAMILY STUDIES

460.150726

505.108521

419.239563


137.059479

178.185425


196.060516


PSYCHOLOGY, APPLIED

1046.133179

213.097046


PHILOSOPHY

106.103317

ETHNIC STUDIES

81.097603

INDUSTRIAL RELATIONS & LABOR

263.091339

COMMUNICATION

229.107361

DEMOGRAPHY

224.119812


346.108307


2064.105469

439.128784

71.034935

2068.419434

LITERATURE, ROMANCE

51.141861

THEATER

LITERARY REVIEWS

38.047237

LITERATURE, SLAVIC

10.131647

ENGINEERING, OCEAN

224.096375

MUSIC

19.014132

LITERATURE

101.068184

124.161316

14.040447POETRY

15.055243


19.053978

ARTS & HUMANITIES, GENERAL130.092987

ARCHITECTURE

9.030687

ART

51.088272

RELIGION

117.064674

Fig. 16 The scientogram of USA in 2002, drawn with the Kamada-Kawai algorithm

16. Mount, D.M., Arya, S.: (2006). ANN: A Library for Approximate Nearest Neighbor Search-ing, version 1.1.1, online software available on http://www.cs.umd.edu/∼mount/ANN/, re-leased the 4/8/2006

17. Moya-Anegón, F., Vargas-Quesada, B., Chinchilla-Rodríguez, Z., Corera-Álvarez, E.,González-Molina, A., Muñoz-Fernández, F., Herrero-Solana, V.: Visualización y análisis dela estructura científica española: ISI web of science 1990-2005 (in Spanish). El Profesionalde la Información 15(4), 258–269 (2006)

18. Moya-Anegón, F., Vargas-Quesada, B., Chinchilla-Rodríguez, Z., Corera-Álvarez, E.,González-Molina, A., Muñoz-Fernández, F., Herrero-Solana, V.: Visualizing the marrow ofscience. Journal of the American Society for Information Science and Technology 58(14),2167–2179 (2007)

19. Moya-Anegón, F., Vargas-Quesada, B., Chinchilla-Rodríguez, Z., Corera-Álvarez, E.,Herrero-Solana, V., Muñoz-Fernández, F.: Domain analysis and information retrieval throughthe construction of heliocentric maps based on ISI-JCR category cocitation. Information Pro-cessing and Management 41, 1520–1533 (2005)

20. Moya-Anegón, F., Vargas-Quesada, B., Herrero-Solana, V., Chinchilla-Rodríguez, Z., Corera-Álvarez, E., Muñoz-Fernández, F.: A new technique for building maps of large scientific do-


29 BIOCHEMISTRY&

MOLECULARBIOLOGY

3 GASTROENTEROLOGY&

HEPATOLOGY

6 MEDICINE,GENERAL

&INTERNAL

9 ENTOMOLOGY


30 PLANTSCIENCES

32 BIOLOGY

33 BIOTECHNOLOGY&

APPLIEDMICROBIOLOGY

35 CRYSTALLOGRAPHY


37 CELLBIOLOGY

38 DERMATOLOGY&

VENEREALDISEASES

39 ENDOCRINOLOGY&

METABOLISM

40 HEMATOLOGY

46 MEDICINE,RESEARCH

&EXPERIMENTAL

47 NEUROSCIENCES

49 PATHOLOGY53 ONCOLOGY

54 OPHTHALMOLOGY58 PHARMACOLOGY&

PHARMACY

60 PHYSIOLOGY

66 PARASITOLOGY

68 VIROLOGY

71 MICROBIOLOGY76 BIOPHYSICS

83 GENETICS&

HEREDITY

84 IMMUNOLOGY

92 GERIATRICS&

GERONTOLOGY

101 UROLOGY&

NEPHROLOGY


120 ANDROLOGY

158 MYCOLOGY

165 MICROSCOPY

34 SURGERY

50 OBSTETRICS&

GYNECOLOGY

57 PEDIATRICS

100 RHEUMATOLOGY


&OCCUPATIONAL

HEALTH


&CRITICAL

CARE

109 MEDICINE,LEGAL

204 HEALTHCARE

SCIENCES&

SERVICES

51 DENTISTRY,ORAL

SURGERY&

MEDICINE

55 ORTHOPEDICS


82 REPRODUCTIVEBIOLOGY


65 TROPICALMEDICINE

161 SOCIALSCIENCES,

BIOMEDICAL

167 TRANSPORTATION

183 NURSING



DISCIPLINES

96 HISTORY&

PHILOSOPHYOF

SCIENCE

197 HEALTHPOLICY

&SERVICES

198 PHILOSOPHY 61 POLYMERSCIENCE




&NUCLEAR



75 PHYSICS,ATOMIC,

MOLECULAR&

CHEMICAL

0 ENERGY&

FUELS

2 ENGINEERING,PETROLEUM


74 OPTICS

132 SPECTROSCOPY

73 PHYSICS,NUCLEAR


MATTER


&FIELDS



MULTIDISCIPLINARY

62 PHYSICS,APPLIED

44 METALLURGY&


45 MECHANICS


COMPOSITES


CERAMICS


CHARACTERIZATION&

TESTING

152 MINING&

MINERALPROCESSING


126 PHYSICS,FLUIDS

&PLASMAS

135 THERMODYNAMICS


&ELECTRONIC


COATINGS&

FILMS

14 COMPUTERSCIENCE,

INFORMATIONSYSTEMS

88 AUTOMATION&

CONTROLSYSTEMS

97 COMPUTERSCIENCE,




HARDWARE&

ARCHITECTURE

15 COMPUTERSCIENCE,

SOFTWARE,GRAPHICS,

PROGRAMMING


&LIBRARYSCIENCE


&METHODS



INTERDISCIPLINARYAPPLICATIONS

210 MUSIC

114 INSTRUMENTS&

INSTRUMENTATION

124 NUCLEARSCIENCE

&TECHNOLOGY


21 AGRICULTURE

145 HORTICULTURE


52 ECOLOGY

110 ANTHROPOLOGY


43 MARINE&

FRESHWATERBIOLOGY

95 FORESTRY

141 ORNITHOLOGY

137 FISHERIES


PAPER&

WOOD

190 ARCHAEOLOGY

72 STATISTICS&

PROBABILITY


172 SOCIALSCIENCES,

MATHEMATICALMETHODS


5 MATHEMATICS

93 ENGINEERING

171 ECONOMICS


&POLICY


164 LAW

173 BUSINESS

177 PLANNING&

DEVELOPMENT




193 HISTORYOF

SOCIALSCIENCES


&LABOR

174 MANAGEMENT


&MANAGEMENT

SCIENCE



175 URBANSTUDIES

215 ARCHITECTURE

185 AREASTUDIES


201 COMMUNICATION

191 HISTORY

207 LITERARYREVIEWS

211 LITERATURE

214 ARTS&

HUMANITIES,GENERAL

195 LANGUAGE&

LINGUISTICS

206 THEATER

212 POETRY



208 LITERATURE,SLAVIC

216 ART

24 FOODSCIENCE

&TECHNOLOGY


&ANIMALSCIENCE


26 ANATOMY&

MORPHOLOGY

23 NUTRITION&

DIETETICS


DISEASE

18 CARDIAC&




31 ZOOLOGY


64 PSYCHIATRY



CYBERNETICS

25 ANESTHESIOLOGY

69 SUBSTANCEABUSE

123 PSYCHOLOGY



131 ERGONOMICS



156 EDUCATION&

EDUCATIONALRESEARCH

176 SOCIALSCIENCES,

INTERDISCIPLINARY




187 CRIMINOLOGY&

PENOLOGY

192 FAMILYSTUDIES

163 SOCIOLOGY

181 SOCIALWORK

179 SOCIALISSUES

199 ETHNICSTUDIES

202 DEMOGRAPHY

217 RELIGION



&MEDICALIMAGING

17 ACOUSTICS

91 TOXICOLOGY




22 AGRICULTURE,SOIL

SCIENCE

42 WATERRESOURCES


138 LIMNOLOGY

28 ASTRONOMY&

ASTROPHYSICS

89 METEOROLOGY&

ATMOSPHERICSCIENCES

103 PALEONTOLOGY

115 GEOCHEMISTRY&

GEOPHYSICS

122 OCEANOGRAPHY

140 GEOGRAPHY

143 GEOLOGY



116 MINERALOGY

166 REMOTESENSING

169 IMAGINGSCIENCE




11 CONSTRUCTION&

BUILDINGTECHNOLOGY


113 SPORTSCIENCES

112 REHABILITATION




BIOMATERIALS



104 ALLERGY

147 TRANSPLANTATION

Fig. 17 The scientogram of USA in 2002, drawn with the Vmap-Layout algorithm

mains based on the cocitation of classes and categories. Scientometrics 61(1), 129–145 (2004)21. Nguyen, Q.V., Huang, M.L.: A space-optimized tree visualization. In: IEEE Symposium on

Information Visualization (InfoVis 2002), pp. 85–92 (2002)22. Parlebas, P.: Centralité et compacité d’un graphe. Mathématiques et Sciences Humaines 39,

5–26 (1972)23. Quirin, A., Cordón, O., Guerrero-Bote, V.P., Vargas-Quesada, B., Moya-Anegón, F.: A quick

MST-based algorithm to obtain pathfinder networks. Journal of the American Society forInformation Science and Technology 59(12), 1912–1924 (2008)

24. Salton, G., Bergmark, D.: A citation study of computer science literature. IEEE Transactionson Professional Communication 22, 146–158 (1979)

25. Small, H., Garfield, E.: The geography of science: disciplinary and national mappings. Journalof Information Science 11, 147–159 (1985)

26. Vargas-Quesada, B., Moya-Anegón, F.: Visualizing the Structure of Science. New York:Springer (2007)

27. Vargas-Quesada, B., Moya-Anegón, F., Chinchilla-Rodríguez, Z., Corera-Álvarez, E.,González-Molina, A., Muñoz-Fernández, F., Herrero-Solana, V.: Evolución de la estructura


ENERGY & FUELS



2248.230957



MATHEMATICS


9020.078125


MEDICAL INFORMATICS

ENTOMOLOGY


2069.062012



714.051514


5690.168945




8856.152344

2286.126709

3265.140137

ACOUSTICS

732.054443


15907.106445

RESPIRATORY SYSTEM

8110.119629


AGRICULTURE

3698.119385


3951.094238



17522.197266

ANESTHESIOLOGY1397.036865





7920.053711

18466.054688

22493.060547

4328.036133

16923.080078

8662.059570

PLANT SCIENCES

27952.093750

ZOOLOGY

13097.062500

BIOLOGY

24623.132812


31845.126953

SURGERY

12207.097656

CRYSTALLOGRAPHY

9251.105469


29587.144531

CELL BIOLOGY

4620.078613

47910.136719

DERMATOLOGY & VENEREAL DISEASES

2978.041992


18945.080078

HEMATOLOGY

12549.101562


5157.088379

11662.054688

WATER RESOURCES 7141.182617



5266.147461

MECHANICS


21643.113281

NEUROSCIENCES

20289.054688

CLINICAL NEUROLOGY

18133.117188

PATHOLOGY14076.133789

OBSTETRICS & GYNECOLOGY7290.055664


854.036926

ECOLOGY

6347.083008

ONCOLOGY

16867.070312

OPHTHALMOLOGY

1473.024292

ORTHOPEDICS

1696.069336

OTORHINOLARYNGOLOGY

1227.057739

PEDIATRICS

6711.092285

PHARMACOLOGY & PHARMACY

31962.101562


3737.058594

PHYSIOLOGY

17725.085938

POLYMER SCIENCE

PHYSICS, APPLIED


6176.153809

PSYCHIATRY

11518.105469

TROPICAL MEDICINE

PARASITOLOGY

VETERINARY SCIENCES

5925.041504

1470.072998

VIROLOGY

SUBSTANCE ABUSE5862.237793


2013.168579

MICROBIOLOGY

15301.054688


7550.183594

PHYSICS, NUCLEAR

8587.083008

OPTICS

10661.154297


15096.089844

BIOPHYSICS

35538.144531

CHEMISTRY, ORGANIC

23058.111328


25175.076172


8517.074219

CHEMISTRY, PHYSICAL

27106.117188

8329.073242

11131.08691420409.113281


2885.156006

REPRODUCTIVE SYSTEMS

2897.025879

GENETICS & HEREDITY

24567.089844IMMUNOLOGY

21488.074219

5727.074219


7259.117188


16836.099609


15076.153320

15753.103516

15555.160156


4776.188965


4459.143555

BEHAVIORAL SCIENCES

8986.111328

TOXICOLOGY

10933.133789


6239.068848

ENGINEERING1842.085327


4869.224609

FORESTRY

4218.100098



3428.121582


317.035522

INFECTIOUS DISEASES

16188.176758

RHEUMATOLOGY

3538.058838


5917.066406

TELECOMMUNICATIONS

2316.127441

PALEONTOLOGY

1488.086548

ALLERGY

3590.074463


12780.234375

8995.136719


4350.130859


10119.111328

1321.104004


3328.067627

MEDICINE, LEGAL

583.046143

ANTHROPOLOGY

908.055847


17780.218750

REHABILITATION

704.032532

SPORT SCIENCES

2044.080688


8235.174805


7222.181152

MINERALOGY

1990.089111


8478.208008


2838.306641

3279.347656


10458.074219

ANDROLOGY

578.098450


OCEANOGRAPHY

4531.102539

PSYCHOLOGY

8031.199707


3865.177246

CHEMISTRY, APPLIED

18755.222656


493.088806


2298.324707

PHYSICS, PARTICLES & FIELDS8121.064453

CHEMISTRY, MEDICINAL

13433.085938

MATERIALS SCIENCE, PAPER & WOOD514.087036

ERGONOMICS

791.129883

SPECTROSCOPY

7549.076660


1469.075317

ENGINEERING, MARINE

217.046021

THERMODYNAMICS

5393.144531


4748.135254

FISHERIES

5238.136230

LIMNOLOGY

2747.101807


5801.163574

GEOGRAPHY

ORNITHOLOGY

1709.058105


3110.145508

GEOLOGY

3197.134277


5032.041016

3619.189697

HORTICULTURE

7232.182617


1117.100098

TRANSPLANTATION 4911.086426


2568.124756


1113.120850

MATERIALS SCIENCE, CHARACTERIZATION & TESTING2076.133545

ENGINEERING, CIVIL

10353.263672


726.061035


6978.138184

8240.10351611448.125977

8365.269531

ELECTROCHEMISTRY

4243.060547


806.084229


305.039185

ENGINEERING, INDUSTRIAL460.141693

MYCOLOGY

2454.075195


643.078857


531.042480


782.097107


2467.173096

SOCIOLOGY

295.044067

LAW

MICROSCOPY

1396.046265

REMOTE SENSING

833.070740

TRANSPORTATION


2660.112061


569.164246


347.038330

ECONOMICS

171.054749SOCIAL SCIENCES, MATHEMATICAL METHODS

2760.203125

2261.177734

BUSINESS

1319.063599

MANAGEMENT

1335.208496

URBAN STUDIES

169.199966

SOCIAL SCIENCES, INTERDISCIPLINARY1036.086792


340.081116

BUSINESS, FINANCE

881.134460

SOCIAL ISSUES

95.010422


54.028301

SOCIAL WORK

128.038071

PSYCHOLOGY, SOCIAL

1256.107300NURSING

571.038574

WOMEN’S STUDIES

54.025826

AREA STUDIES

29.023806

POLITICAL SCIENCE

187.052582


75.030243


91.040588

EDUCATION, SPECIAL

173.182587

ARCHAEOLOGY

392.052399

HISTORY

FAMILY STUDIES

125.052017


99.046104


165.035324


530.074646

PSYCHOLOGY, APPLIED 647.082886


PHILOSOPHY

98.005898

130.107117

ETHNIC STUDIES

11.058056

INDUSTRIAL RELATIONS & LABOR

138.059586

COMMUNICATION

1691.055542

DEMOGRAPHY

107.111656


413.062347


6213.300293

1117.213379

LITERATURE, ROMANCE

215.112915

THEATER

10.046248

LITERARY REVIEWS

50.101940

ENGINEERING, OCEAN

290.438904

MUSIC

24.011345

LITERATURE

149.092834

POETRY

4.004330


7.005567


577.051514

110.049355

ARCHITECTURE

9.046108

ART

119.132202

RELIGION

144.126450

FOLKLORE

8.026299

FILM, RADIO, TELEVISION

13.002386

CLASSICS

27.038807

ASIAN STUDIES

22.103058

LITERATURE, GERMAN, NETHERLANDIC, SCANDINAVIAN

LITERATURE, BRITISH ISLES

10.027319

LITERATURE, AFRICAN, AUSTRALIAN, CANADIAN

4.068022

AGRICULTURE, MULTIDISCIPLINARY

10512.234375

ROBOTICS

443.136993

ETHICS

232.313339

TRANSPORTATION SCIENCE & TECHNOLOGY

150.027374

338.481079

APPLIED LINGUISTICS

831.265564

INTEGRATIVE & COMPLEMENTARY MEDICINE

299.031677

BIODIVERSITY CONSERVATION

5377.175781

PSYCHOLOGY, MULTIDISCIPLINARY

4905.257324

LITERARY THEORY & CRITICISM

129.186905

2.059080

CRITICAL CARE MEDICINE

4064.350830

GERONTONLOGY

1117.204956

MEDICAL ETHICS

66.013374

NEUROIMAGING

2931.129883

AGRICULTURAL ENGINEERING

1659.107666

EVOLUTIONARY BIOLOGY

7946.212402

GEOGRAPHY, PHYSICAL

2498.150146

1744.365601

Fig. 18 The scientogram of Spain in 2002, drawn with the Kamada-Kawai algorithm

científica española: ISI web of science 1990-2005 (in Spanish). El Profesional de la Informa-ción (2007). In press

28. Vargas-Quesada, B., Moya-Anegón, F., Chinchilla-Rodríguez, Z., González-Molina, A.:Showing the essential science structure of a scientific domain and its evolution. InformationVisualization (2007). In press


29 BIOCHEMISTRY&

MOLECULARBIOLOGY


&MEDICALIMAGING

6 MEDICINE,GENERAL

&INTERNAL



&ANIMALSCIENCE

21 AGRICULTURE

23 NUTRITION&

DIETETICS

30 PLANTSCIENCES

31 ZOOLOGY

32 BIOLOGY

33 BIOTECHNOLOGY&

APPLIEDMICROBIOLOGY


37 CELLBIOLOGY

39 ENDOCRINOLOGY&

METABOLISM

41 ENVIRONMENTALSCIENCES46 MEDICINE,

RESEARCH&

EXPERIMENTAL

47 NEUROSCIENCES

50 OBSTETRICS&

GYNECOLOGY

53 ONCOLOGY

58 PHARMACOLOGY&

PHARMACY

60 PHYSIOLOGY


71 MICROBIOLOGY

76 BIOPHYSICS



82 REPRODUCTIVESYSTEMS

83 GENETICS&

HEREDITY

84 IMMUNOLOGY

92 GERIATRICS&

GERONTOLOGY





218 FILM,RADIO,

TELEVISION

17 ACOUSTICS

3 GASTROENTEROLOGY&

HEPATOLOGY

18 CARDIAC&


25 ANESTHESIOLOGY

34 SURGERY

38 DERMATOLOGY&

VENEREALDISEASES

40 HEMATOLOGY

57 PEDIATRICS

100 RHEUMATOLOGY

101 UROLOGY&

NEPHROLOGY


&OCCUPATIONAL

HEALTH


&CRITICAL

CARE

112 REHABILITATION

179 SOCIALISSUES

183 NURSING

198 PHILOSOPHY

235 MEDICALETHICS



DISEASE

51 DENTISTRY,ORAL

SURGERY&

MEDICINE

55 ORTHOPEDICS


211 POETRY

65 TROPICALMEDICINE

161 SOCIALSCIENCES,

BIOMEDICAL

204 HEALTHCARE

SCIENCES&

SERVICES

202 DEMOGRAPHY

197 HEALTHPOLICY

&SERVICES

233 CRITICALCARE

MEDICINE


96 HISTORY&

PHILOSOPHYOF

SCIENCE

226 ETHICS


DISCIPLINES

35 CRYSTALLOGRAPHY




&NUCLEAR

132 SPECTROSCOPY

61 POLYMERSCIENCE


75 PHYSICS,ATOMIC,

MOLECULAR&

CHEMICAL


BIOMATERIALS


CHARACTERIZATION&

TESTING

0 ENERGY&

FUELS2 ENGINEERING,

PETROLEUM


45 MECHANICS73 PHYSICS,NUCLEAR


MATTER


&FIELDS


201 COMMUNICATION



MULTIDISCIPLINARY

62 PHYSICS,APPLIED

11 CONSTRUCTION&

BUILDINGTECHNOLOGY

44 METALLURGY&



COMPOSITES98 ENGINEERING,

MANUFACTURING


CERAMICS


COATINGS&

FILMS

74 OPTICS


&ELECTRONIC

114 INSTRUMENTS&

INSTRUMENTATION

135 THERMODYNAMICS

97 COMPUTERSCIENCE,




CYBERNETICS

227 TRANSPORTATIONSCIENCE

&TECHNOLOGY

131 ERGONOMICS

167 TRANSPORTATION

124 NUCLEARSCIENCE

&TECHNOLOGY

5 MATHEMATICS

28 ASTRONOMY&

ASTROPHYSICS

126 PHYSICS,FLUIDS

&PLASMAS


&METHODS



15 COMPUTERSCIENCE,

SOFTWARE,GRAPHICS,

PROGRAMMING

72 STATISTICS&

PROBABILITY

88 AUTOMATION&

CONTROLSYSTEMS

93 ENGINEERING


&MANAGEMENT

SCIENCE



HARDWARE&

ARCHITECTURE14 COMPUTER

SCIENCE,INFORMATION

SYSTEMS127 INFORMATIONSCIENCE

&LIBRARYSCIENCE

225 ROBOTICS


174 MANAGEMENT

172 SOCIALSCIENCES,

MATHEMATICALMETHODS

171 ECONOMICS

164 LAW

177 PLANNING&

DEVELOPMENT



185 AREASTUDIES



193 HISTORYOF

SOCIALSCIENCES


&LABOR


9 ENTOMOLOGY

22 AGRICULTURE,SOIL

SCIENCE

24 FOODSCIENCE

&TECHNOLOGY


&POLICY

145 HORTICULTURE224 AGRICULTURE,MULTIDISCIPLINARY237 AGRICULTURAL

ENGINEERING



95 FORESTRY


PAPER&

WOOD


176 SOCIALSCIENCES,

INTERDISCIPLINARY

52 ECOLOGY

110 ANTHROPOLOGY

213 ARTS&

HUMANITIES,GENERAL

238 EVOLUTIONARYBIOLOGY

43 MARINE&

FRESHWATERBIOLOGY

141 ORNITHOLOGY

230 BIODIVERSITYCONSERVATION

122 OCEANOGRAPHY

137 FISHERIES

138 LIMNOLOGY



191 HISTORY

232 LITERARYTHEORY

&CRITICISM

216 RELIGION

219 CLASSICS

220 ASIANSTUDIES

221 LITERATURE,GERMAN,

NETHERLANDIC,SCANDINAVIAN

26 ANATOMY&

MORPHOLOGY

49 PATHOLOGY

165 MICROSCOPY

109 MEDICINE,LEGAL


42 WATERRESOURCES




173 BUSINESS

89 METEOROLOGY&

ATMOSPHERICSCIENCES

103 PALEONTOLOGY

115 GEOCHEMISTRY&

GEOPHYSICS

143 GEOLOGY152 MINING

&MINERAL

PROCESSING

190 ARCHAEOLOGY


239 GEOGRAPHY,PHYSICAL

116 MINERALOGY

166 REMOTESENSING

169 IMAGINGSCIENCE


214 ARCHITECTURE

215 ART

140 GEOGRAPHY

175 URBANSTUDIES


54 OPHTHALMOLOGY

64 PSYCHIATRY


236 NEUROIMAGING

69 SUBSTANCEABUSE

123 PSYCHOLOGY






156 EDUCATION&

EDUCATIONALRESEARCH159 PSYCHOLOGY,

EDUCATIONAL

163 SOCIOLOGY

181 SOCIALWORK



187 CRIMINOLOGY&

PENOLOGY


231 PSYCHOLOGY,MULTIDISCIPLINARY

195 LANGUAGE&

LINGUISTICS


210 LITERATURE

222 LITERATURE,BRITISH

ISLES

228 APPLIEDLINGUISTICS

206 THEATER

207 LITERARYREVIEWS

217 FOLKLORE

223 LITERATURE,AFRICAN,

AUSTRALIAN,CANADIAN

199 ETHNICSTUDIES

192 FAMILYSTUDIES


91 TOXICOLOGY

229 INTEGRATIVE&

COMPLEMENTARYMEDICINE

113 SPORTSCIENCES


66 PARASITOLOGY

158 MYCOLOGY


120 ANDROLOGY

68 VIROLOGY


104 ALLERGY

147 TRANSPLANTATION

234 GERONTONLOGY


209 MUSIC

Fig. 19 The scientogram of Spain in 2002, drawn with the Vmap-Layout algorithm


ENERGY & FUELS


56.206600

ENGINEERING, PETROLEUM54.346268



MATHEMATICS



MEDICAL INFORMATICS

ENTOMOLOGY


42.081261



7.036361





21.106098

ACOUSTICS


RESPIRATORY SYSTEM

63.162621


AGRICULTURE

445.239441


71.107300



305.240265

ANESTHESIOLOGY





66.049622

162.068527

336.087494

469.102478

249.088577

115.068436

PLANT SCIENCES

463.131470

ZOOLOGY

144.076477

BIOLOGY

353.230804

8.047099

419.143646


812.187439

SURGERY

CRYSTALLOGRAPHY

129.101807


742.213806

CELL BIOLOGY

804.224121DERMATOLOGY & VENEREAL DISEASES

37.046200


307.123962

HEMATOLOGY

179.231232


172.082474

WATER RESOURCES



72.123489

MECHANICS


455.134216

NEUROSCIENCES

95.136589

310.066895

CLINICAL NEUROLOGY

11.038918

162.129791

512.183777

PATHOLOGY

217.113602


123.059586


ECOLOGY

50.128109

ONCOLOGY

317.109741

OPHTHALMOLOGY41.055393

ORTHOPEDICS

19.121214

OTORHINOLARYNGOLOGY

31.049795

PEDIATRICS

77.104179PHARMACOLOGY & PHARMACY

620.133484


PHYSIOLOGY

222.087158

POLYMER SCIENCE

113.077866

PHYSICS, APPLIED

83.127602


72.190498

142.112762

PSYCHIATRY

201.203598

TROPICAL MEDICINE

PARASITOLOGY

94.117149

VETERINARY SCIENCES

74.178772

176.083893

VIROLOGY

157.065765


21.235451

MICROBIOLOGY

380.114380


355.591766

PHYSICS, NUCLEAR

88.083351

OPTICS189.192841


BIOPHYSICS

661.208191

CHEMISTRY, ORGANIC

329.179565


589.149963


CHEMISTRY, PHYSICAL

330.141022

253.169739


44.169064

REPRODUCTIVE SYSTEMS

39.033215

GENETICS & HEREDITY

376.120392

IMMUNOLOGY

602.145325


26.082359

235.199951


136.134201


403.183014

390.146759

530.179932

222.082108


34.160007


43.214520

BEHAVIORAL SCIENCES

155.163345

TOXICOLOGY

279.184753


124.152466

ENGINEERING

FORESTRY

45.118618


9.048798


27.113920


5.081934

INFECTIOUS DISEASES

316.230255

RHEUMATOLOGY

16.022116


18.036581

TELECOMMUNICATIONS

10.194037

PALEONTOLOGY

ALLERGY

47.093735


460.473755

100.190582


88.197083


184.138901

109.185196


27.076044

MEDICINE, LEGAL

11.042807

ANTHROPOLOGY

13.071912


315.366516

REHABILITATION

12.051997


140.152817

25.150686


74.262451

MINERALOGY

28.183559


104.292686


23.436769


54.061970

ANDROLOGY

4.110558


122.098595

OCEANOGRAPHY

26.146170

PSYCHOLOGY

180.137863


56.171089

CHEMISTRY, APPLIED

270.355896




85.113953

CHEMISTRY, MEDICINAL

382.218414

163.259689

MATERIALS SCIENCE, PAPER & WOOD

9.155799

SPECTROSCOPY

109.101227


7.062321

THERMODYNAMICS

121.192368


130.157471

FISHERIES

64.194313

LIMNOLOGY

8.184017


373.606842

357.523590

GEOGRAPHY

4.084972

ORNITHOLOGY


6.067420

85.235374

GEOLOGY

33.190098


163.113556

97.180801

93.174675

HORTICULTURE

83.182480


31.076740

TRANSPLANTATION

40.190964


99.076813


16.144356


51.157543

ENGINEERING, CIVIL

157.389771

83.338211


8.216533


96.298546

104.299820

141.152054

110.455650ELECTROCHEMISTRY

85.340591


13.037610


1.250000

ENGINEERING, INDUSTRIAL

6.341882

MYCOLOGY

67.089127


5.246933


10.079591


14.053674


87.212204

SOCIOLOGY

4.030184

MICROSCOPY

9.025423

REMOTE SENSING

3.433013

4.098117


20.056499


5.064336


1.042333

BUSINESS

18.362915

MANAGEMENT

3.307794

URBAN STUDIES


4.091526


SOCIAL ISSUES

7.045216

SOCIAL WORK

1.117041

PSYCHOLOGY, SOCIAL

3.038289

WOMEN’S STUDIES

2.033768

AREA STUDIES

POLITICAL SCIENCE

4.031292

3.4242645.707107



2.400000

ARCHAEOLOGY

3.088542

HISTORY

2.025902

FAMILY STUDIES



21.125357

PHILOSOPHY

ETHNIC STUDIES

DEMOGRAPHY

14.079908

17.478920


2.069631


105.285713

LITERATURE, ROMANCE

THEATER

1.192450

LITERARY REVIEWS

1.064550

LITERATURE

1.068519


13.094835

ARCHITECTURE

ART

RELIGION

MATHEMATICS, PURE

41.278168

COMPUTER APPLICATIONS, CHEMISTRY & ENGINEERING

114.206345

MATHEMATICAL METHODS, BIOLOGY & MEDICINE

30.320530

76.242722

MATHEMATICAL METHODS, PHYSICAL SCIENCES

104.411354

MATHEMATICS, GENERAL

46.304474

CONTROL THEORY & CYBERNETICS

18.390200

COMPUTER SCIENCES, SPECIAL TOPICS

27.325466

SYSTEMS SCIENCE

6.220564

FOLKLORE

1.052271

LITERATURE, AFRICAN, AUSTRALIAN, CANADIAN

AGRICULTURE, MULTIDISCIPLINARY

166.240005

ROBOTICS

1.316228

ETHICS

8.303895

6.377964

APPLIED LINGUISTICS

24.123737

26.379814

INTEGRATIVE & COMPLEMENTARY MEDICINE

28.078924

BIODIVERSITY CONSERVATION

8.188144

53.174431

11.135875

PSYCHOLOGY, MULTIDISCIPLINARY

52.220577

LITERARY THEORY & CRITICISM

CRITICAL CARE MEDICINE

35.589256

GERONTONLOGY

15.228403

MEDICAL ETHICS

6.414039

NEUROIMAGING

154.178299

AGRICULTURAL ENGINEERING

56.139942

EVOLUTIONARY BIOLOGY

76.191391

Fig. 20 The scientogram of Cuba in 2002, drawn with the Kamada-Kawai algorithm


29 BIOCHEMISTRY&

MOLECULARBIOLOGY

3 GASTROENTEROLOGY&

HEPATOLOGY


&MEDICALIMAGING

6 MEDICINE,GENERAL

&INTERNAL


18 CARDIAC&


23 NUTRITION&

DIETETICS

30 PLANTSCIENCES

31 ZOOLOGY

32 BIOLOGY

33 BIOTECHNOLOGY&

APPLIEDMICROBIOLOGY


37 CELLBIOLOGY

38 DERMATOLOGY&

VENEREALDISEASES

39 ENDOCRINOLOGY&

METABOLISM


46 MEDICINE,RESEARCH

&EXPERIMENTAL

47 NEUROSCIENCES

49 PATHOLOGY

50 OBSTETRICS&

GYNECOLOGY

53 ONCOLOGY

58 PHARMACOLOGY&

PHARMACY

60 PHYSIOLOGY


68 VIROLOGY

70 MICROBIOLOGY

75 BIOPHYSICS


81 REPRODUCTIVESYSTEMS

82 GENETICS&

HEREDITY

83 IMMUNOLOGY

98 RHEUMATOLOGY


159 MICROSCOPY

57 PEDIATRICS

94 HISTORY&

PHILOSOPHYOF

SCIENCE

99 UROLOGY&

NEPHROLOGY


&OCCUPATIONAL

HEALTH


&CRITICAL

CARE

107 MEDICINE,LEGAL

156 SOCIALSCIENCES,

BIOMEDICAL

65 TROPICALMEDICINE




181 HEALTHPOLICY

&SERVICES

184 DEMOGRAPHY

186 HEALTHCARE

SCIENCES&

SERVICES

179 FAMILYSTUDIES

213 CRITICALCARE

MEDICINE

207 ETHICS

182 PHILOSOPHY

215 MEDICALETHICS


DISCIPLINES

35 CRYSTALLOGRAPHY

61 POLYMERSCIENCE




128 SPECTROSCOPY




BIOMATERIALS

51 DENTISTRY,ORAL

SURGERY&

MEDICINE

0 ENERGY&

FUELS



2 ENGINEERING,PETROLEUM

88 METEOROLOGY&

ATMOSPHERICSCIENCES

112 GEOCHEMISTRY&

GEOPHYSICS

138 GEOLOGY

177 ARCHAEOLOGY

113 MINERALOGY

135 GEOGRAPHY

160 REMOTESENSING

151 EDUCATION&

EDUCATIONALRESEARCH


147 MINING&

MINERALPROCESSING

74 PHYSICS,ATOMIC,

MOLECULAR&

CHEMICAL


&NUCLEAR


MATTER

121 NUCLEARSCIENCE

&TECHNOLOGY


MULTIDISCIPLINARY


62 PHYSICS,APPLIED

11 CONSTRUCTION&

BUILDINGTECHNOLOGY

44 METALLURGY&



COMPOSITES


CERAMICS


CHARACTERIZATION&

TESTING



164 BUSINESS

72 PHYSICS,NUCLEAR


&FIELDS

45 MECHANICS

73 OPTICS


&ELECTRONIC

111 INSTRUMENTS&

INSTRUMENTATION

130 THERMODYNAMICS


COATINGS&

FILMS



17 ACOUSTICS

95 COMPUTERSCIENCE,


162 IMAGINGSCIENCE


201 COMPUTERSCIENCES,SPECIALTOPICS

202 SYSTEMSSCIENCE

206 ROBOTICS

92 ENGINEERING


5 MATHEMATICS

28 ASTRONOMY&

ASTROPHYSICS

123 PHYSICS,FLUIDS

&PLASMAS

198 MATHEMATICALMETHODS,PHYSICALSCIENCES

195 MATHEMATICS,PURE

199 MATHEMATICS,GENERAL

14 COMPUTERSCIENCE,

INFORMATIONSYSTEMS


&LIBRARYSCIENCE

196 COMPUTERAPPLICATIONS,

CHEMISTRY&

ENGINEERING


40 HEMATOLOGY


DISEASE140 HORTICULTURE

153 MYCOLOGY

21 AGRICULTURE

26 ANATOMY&

MORPHOLOGY



&ANIMALSCIENCE

22 AGRICULTURE,SOIL

SCIENCE

24 FOODSCIENCE

&TECHNOLOGY 93 FORESTRY

205 AGRICULTURE,MULTIDISCIPLINARY

217 AGRICULTURALENGINEERING



PAPER&

WOOD

52 ECOLOGY

108 ANTHROPOLOGY


191 ARTS&

HUMANITIES,GENERAL

197 MATHEMATICALMETHODS,BIOLOGY

&MEDICINE

210 BIODIVERSITYCONSERVATION

218 EVOLUTIONARYBIOLOGY

43 MARINE&

FRESHWATERBIOLOGY

119 OCEANOGRAPHY

132 FISHERIES

133 LIMNOLOGY188 THEATER

189 LITERARYREVIEWS


15 COMPUTERSCIENCE,

SOFTWARE,GRAPHICS,

PROGRAMMING

71 STATISTICS&

PROBABILITY

87 AUTOMATION&

CONTROLSYSTEMS


&MANAGEMENT

SCIENCE


HARDWARE&

ARCHITECTURE

178 HISTORY

165 MANAGEMENT


170 SOCIALWORK

101 PALEONTOLOGY

136 ORNITHOLOGY


168 PLANNING&

DEVELOPMENT

173 AREASTUDIES




42 WATERRESOURCES


66 PARASITOLOGY


&METHODS


54 OPHTHALMOLOGY56 OTORHINOLARYNGOLOGY89 BEHAVIORAL

SCIENCES91 GERIATRICS

&GERONTOLOGY

120 PSYCHOLOGY


CYBERNETICS




216 NEUROIMAGING


25 ANESTHESIOLOGY

34 SURGERY

64 PSYCHIATRY

110 REHABILITATION


169 SOCIALISSUES

55 ORTHOPEDICS

142 TRANSPLANTATION

203 FOLKLORE

214 GERONTONLOGY


211 PSYCHOLOGY,MULTIDISCIPLINARY

200 CONTROLTHEORY

&CYBERNETICS

208 APPLIEDLINGUISTICS

180 LANGUAGE&

LINGUISTICS

190 LITERATURE


90 TOXICOLOGY


158 SOCIOLOGY

209 INTEGRATIVE&

COMPLEMENTARYMEDICINE



167 SOCIALSCIENCES,

INTERDISCIPLINARY

9 ENTOMOLOGY

117 ANDROLOGY


102 ALLERGY

Fig. 21 The scientogram of Cuba in 2002, drawn with the Vmap-Layout algorithm

vmap-layout, a layout algorithm for drawing scientograms

Documents