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  • Lab 4: Working with NetDrawOpening a datasetFile>OpenEditing node attributesTransform>Node attribute editorEditing link propertiesProperties>LinesConfiguring networksLayout>Highlighting parts of the networkAnalysis>Storing the dataset or the diagramFile>Save

    Using an external editor (Notepad) to edit a NetDraw dataset (a .vna file)

  • *The Development of Social Network Analysiswith an Emphasis on Recent Events (Freeman, 2011)Group Level (Macro Level)Cohesive Subgroups or CommunitiesIndividual Level (Micro Level)PositionCentralities

    In-between (Meso Level)Blockmodeling

  • *Cohesive Subgroups

  • CliqueCohesive subgroups are subgraphs that are more tightly interconnected embedded within a graph.Clique is a subgraph that contains at least three nodes and all the shortest path lengths between nodes are one.

    1365427Clique:{1,2,3}{1,3,4}{3,4,6,7}

  • Loosely-Connected SubgroupsA clique is a fully connected subgraph and the most tightly-connected cohesive subgroup.

    We can release the constrain of the clique:Based on path lengthn-cliquen-clanBased on node degreek-plexk-core

  • N-Cliquen-cliqued(i, j) n for all i, jV1264532-cliquesand{1,2,3,4,5}{2,3,4,5,6 }

  • N-clann-clanconsiders only the shortest paths that pass through the nodes within the subgraph of n-clan and requires all the shortest path lengths be not greater than n.

    An n-clan is also an n-clique, but an n-clique may not be an n-clan.1264532-clan{2,3,4,5,6 }

  • K-plexk-plex is a subgraph that has s nodes, and each node connects to at least other s-k nodes of the subgraph:d(i)(s-k) for all i V31422-plex{1,2,3,4}

  • K-corek-core is a subgraph that each node connects to at least other k nodes of the subgraph: d(i)k for all i V31422-core{1,2,3,4}

  • *Network Data CollectionWhole NetworkPartial NetworkEgo NetworksData Structures: adjacency matrix or adjacency list

  • *Collecting Network from BlogosphereHomepage ()Blogroll

    Post ()Citation (hyperlink in content)TrackbackComment

    Select Top 100 blogsin 2008, 2009, 2010, 2011 fromhttp://look.urs.tw (Closed Now)

  • *

    A Blogroll Network (2008)Top 100 + Random 100 Blogroll Network

  • Analysis of CliquesComponent of Cliques

    Number of Cliques3-node cliques4-node cliques4-node cliques6741224

  • The Largest Cliques

    Cliquemember118103340217485575973485575929744871759297

  • Lab 5: Finding all the cliques outNetwork>Subgroups>CliquesInput dataset:2008.vna

    Output dataset:

    Interpret the output datasetHierarchical clustering http://www.analytictech.com/networks/hiclus.htm

    Visualize the result in NetDaw

  • Analysis of 2-clique and 2-clanThe largest 2-clique and 2-clan

  • Analysis of 2-plexThe largest 2-plex

    2-plexmember11748557592972485571759297

  • Lab 6: Finding n-cliques, n-clans and k-plexNetwork>Subgroups>Input dataset:2008.vna

    Output dataset:

    Interpret the output dataset

    Visualize the result in NetDaw

  • * Analysis of k-cores

  • * Comparison of Cohesive Subgroups

    Number of nodesNumber of edgesReciprocal edgesAverage degreePath lengthClustering coefficientclique (1) 5103411clique (2) 5106411clique (3) 5106411clique (4) 510104112-clique 225294.7271.9320.5192-clan 225294.7271.9320.5192-plex (1) 61494.6671.0670.9332-plex (2) 614104.6671.0670.9335-core 1450247.1431.5670.424

  • *Inclusion Property of K-corek-coreinclusionc-core(c-1)-core

  • *2008 Blogroll Network

  • *2009 Blogroll Network

  • *K-core Analysis for Exploring Network ChangesIf a node belongs to c-core, but not (c+1)-core, then the coreness of the nodes is c.Coreness change between 2008 and 2009:

    coreness

    coreness2009/9/11012345672008/11/101089805031161410002046210013021740004111114307500102900600000000700000000

  • Lab 7: Analyzing k-coreInput dataset:2008.vna

    Analyzing:In UCINETIn NetDraw

    Interpret the output dataset

  • *Reciprocity, Transitivity, and Closure

  • *On the Second Thought: Open vs. Closed

  • *Structural Hole

  • *Structural Holes

  • *Triad types andBalance-theoreticModels

  • Lab 8: Conducting Triad CensusNetwork>Triad CensusInput dataset:2008.vna

    Output dataset:

    Interpret the output dataset

  • Suggested Readings (ftp://163.25.117.117/nplu)In the directory: //Readings17 The Development of Social Network Analysis.pdf18 Analysing Social Networks Via the Internet.pdf19 Graph Theoretical Approaches to Social Network Analysis.pdf

  • *Centralities

  • *BackgroundAt the individual level, one dimension of position in the network can be captured through centrality.

    Conceptually, centrality is fairly straight forward: we want to identify which nodes are in the center of the network. In practice, identifying exactly what we mean by center is somewhat complicated.

    Approaches:DegreeClosenessBetweennessPower

    The graph level measures: Centralization

  • Degree CentralityAn index that measures the degree of a nodeA local measureABCDEFGHJIKML

  • *Formula of Degree Centralityin-degree centrality:

    out-degree centrality: normalized in-degree centrality:

    normalized out-degree centrality:

  • *Degree Centrality in the Examples

  • *Another ExampleDegree centrality, however, can be deceiving, because it is a purely local measure.

  • Closeness CentralityAn index that measures the distance from a node to the other nodesA global measureABCDEFGHJIKML

  • *Formula of Closeness Centralityi (in-closeness centrality)

    i (out-closeness centrality) i

    i

  • Betweenness CentralityAn index that measures the intermediate importance of a nodeA global measureABCDEFGHJIKML

  • *Formula of Betweenness Centralitybetweenness centrality:

    normalized betweenness centrality:

  • *Betweenness Centrality in the Examples

  • *Centralization of NetworkIf we want to measure the degree to which the graph as a whole is centralized, we look at the dispersion of centrality:Simple: variance of the individual centrality scores.Or, using Freemans general formula for centralization (which ranges from 0 to 1):

  • Centralization of NetworkThe ration CG :

    0CG1

  • *Degree CentralizationFreeman: .07Variance: .20Freeman: 1.0Variance: 3.9Freeman: .02Variance: .17Freeman: 0.0Variance: 0.0

  • *Homework Closeness centralizationBetweenness centralization

  • *ComparisonComparing across these 3 centrality valuesGenerally, the 3 centrality types will be positively correlatedWhen they are not (low) correlated, it probably tells you something interesting about the network.

  • Lab 9: Calculating CentralityNetwork>Centrality and PowerDegreeClosenessBetweenness

  • Centrality Analysisof the BlogosphereData:200820092010

  • *Results of Degree Centralities

  • *Results of Closeness Centralities

  • *Results of Betweenness Centralities

  • *CentralityComparisonofBlogCommunities

  • Results of Network Centralization

    Centralization

    NetworkIn degreeCentralityOut degreeCentralityIn closenessCentralityOut closenessCentralityBetweennessCentrality2008/11/17.79%16.21%20.75%52.36%8.29%2009/9/119.00%12.28%19.78%53.03%5.73%2010/7/27.03%10.46%22.38%55.39%6.51%

  • *The Webs Bowtie Structure

  • *The Bowtie Structure of the 2008 Blogosphere

  • Lab 10: Exploring the Bowtie StructureExcluding disconnected components, we can find out the the bowtie structure of the LWCC:SCCINOUTTendril = LWCC SCC IN OUT

  • *Bonacich Power CentralityActors centrality (prestige) is equal to a function of the prestige of those they are connected to. Thus, actors who are tied to very central actors should have higher prestige/centrality than those who are not. a is a scaling vector, which is set to normalize the score. b reflects the extent to which you weight the centrality of people ego is tied to.R is the adjacency matrix (can be valued)I is the identity matrix (1s down the diagonal) 1 is a matrix of all ones.

  • *The Parameter: bThe magnitude of b reflects the radius of power.Small values of b weight local structure,Larger values weight global structure.

    If b is positive, then ego has higher centrality when tied to people who are central.

    If b is negative, then ego has higher centrality when tied to people who are not central.

    As b approaches zero, you get degree centrality.

  • *Example

  • *Two Key Dimensions of Centrality (Borgatti, 2003; 2005)The key question for centrality is knowing what is flowing through the network. The key features are:Whether the actor retains the good to pass to others or whether they pass the good and then loose it.Whether the key factor for spread is distance or multiple sources.

    RadialMedialFrequencyDistanceDegree CentralityBon. Power centralityCloseness CentralityBetweenness(empty: but would be an interruption measure based on distance)

  • Suggested Readings (ftp://163.25.117.117/nplu)In the directory: //Readings20 Identifying the role that animals play in their social networks.pdf21 Graph structure in the Web.pdf

  • *Blockmodeling

  • *BlockmodelingThrough row column permutation, adjust adjacency matrix to form compact blocks:0-block1-blockSocial structure emerges from blockmodelingDiagonal blockintra group (community) relationshipOff-diagonal blockinter group (community) relationship

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