mining complex data - networks - ugrelvex.ugr.es/decsai/intelligent/slides/dm/d6 networks.pdf ·...

NetworksNetworks© Fernando Berzal© Fernando Berzal [email protected]@acm.org

NetworksNetworks

�� Network AnalysisNetwork Analysis�� ApplicationsApplications

�� Network PropertiesNetwork Properties

�� Network ModelsNetwork Models�� RandomRandom--Graph ModelsGraph Models

�� Growing Random ModelsGrowing Random Models

�� Strategic Network FormationStrategic Network Formation

�� Network Structure & DynamicsNetwork Structure & Dynamics�� Diffusion through NetworksDiffusion through Networks

�� Search on NetworksSearch on Networks

�� Social Influence ModelsSocial Influence Models

�� Networked MarketsNetworked Markets

�� BibliographyBibliography 11

Network Network AnalysisAnalysis

Networks permeate our lives.Networks permeate our lives.

Networks play a central role in determiningNetworks play a central role in determiningNetworks play a central role in determiningNetworks play a central role in determining

�� the transmission of information about job opportunities,the transmission of information about job opportunities,

�� how diseases spread,how diseases spread,

�� which products we buy,which products we buy,

�� our likelihood of succeeding professionally,our likelihood of succeeding professionally,

�� ……

22


As a field of study…As a field of study…

�� How relationships between parts give rise to the How relationships between parts give rise to the collective behaviors of a system and how the system collective behaviors of a system and how the system collective behaviors of a system and how the system collective behaviors of a system and how the system interacts and forms relationships with its environment interacts and forms relationships with its environment (complex systems).(complex systems).

�� Common principles, algorithms and tools that govern Common principles, algorithms and tools that govern network behavior (network science). network behavior (network science).

33

Origins: Graph TheoryOrigins: Graph Theory


The Seven Bridges of KönisbergThe Seven Bridges of Könisberg

(Leonhard Euler, 1736) (Leonhard Euler, 1736) 44


Networks as graphs “on steroids”…Networks as graphs “on steroids”…

�� ObjectsObjects: Graph vertices.: Graph vertices.

�� Objects can be of different kinds.Objects can be of different kinds.

�� Objects can be labeled.Objects can be labeled.�� Objects can be labeled.Objects can be labeled.

�� Objects can have attributesObjects can have attributes

�� LinksLinks between objects: Graph edges. between objects: Graph edges.

�� Links can be of different kinds.Links can be of different kinds.

�� Links can be directed (arcs) or undirected (edges).Links can be directed (arcs) or undirected (edges).

�� Links can have attributes.Links can have attributes.55

A formal definition of network A formal definition of network

[Ted G. Lewis: “Network Science,” 2009][Ted G. Lewis: “Network Science,” 2009]

G(t) = { N(t), L(t), f(t) : J(t) }G(t) = { N(t), L(t), f(t) : J(t) }


wherewhere t = time (simulated or real)t = time (simulated or real)

N = nodes (a.k.a. vertices or “actors”)N = nodes (a.k.a. vertices or “actors”)

L = links (a.k.a. edges)L = links (a.k.a. edges)

f = topology (connections through links)f = topology (connections through links)

J = behavior of nodes and links (algorithm)J = behavior of nodes and links (algorithm)

66


An interdisciplinary field: Complex systems An interdisciplinary field: Complex systems

(“networks of heterogeneous components that interact”)(“networks of heterogeneous components that interact”)

�� Physics: Physics: Nonlinear dynamics & chaosNonlinear dynamics & chaos..Dynamical systems that are highly sensitive to initial conditions Dynamical systems that are highly sensitive to initial conditions Dynamical systems that are highly sensitive to initial conditions Dynamical systems that are highly sensitive to initial conditions (a.k.a. butterfly effect).(a.k.a. butterfly effect).

�� Economics: Economics: MarketsMarkets..Spontaneous (or emergent) order as the result of human action, Spontaneous (or emergent) order as the result of human action, but not the execution of any human design [Austrian perspective].but not the execution of any human design [Austrian perspective].

�� Information theory: Information theory: Complex adaptive systemsComplex adaptive systems..(focus on the ability to change and learn from experience).(focus on the ability to change and learn from experience). 77

ApplicationsApplications

�� “Cheminformatics”: Chemical compounds.“Cheminformatics”: Chemical compounds.

�� “Bioinformatics”: Protein networks & bio“Bioinformatics”: Protein networks & bio--pathwayspathways

�� Software Engineering: Program analysis…Software Engineering: Program analysis…

�� Network flow analysis (transport, workflows…)Network flow analysis (transport, workflows…)�� Network flow analysis (transport, workflows…)Network flow analysis (transport, workflows…)

�� SemiSemi--structured databases, e.g. XMLstructured databases, e.g. XML

�� Knowledge management: Ontologies & semantic netsKnowledge management: Ontologies & semantic nets

�� ComputerComputer--aided design (CAD): IC design…aided design (CAD): IC design…

�� Geographic information systems (GIS) & cartographyGeographic information systems (GIS) & cartography

�� Social networks, e.g. WebSocial networks, e.g. Web

�� Economic networks, e.g. marketsEconomic networks, e.g. markets88


“Life complexity pyramid”“Life complexity pyramid”

99from

Z.N

. O

ltva

i and A

.-L.

Bara

basi

. S

cience

, 2002


Biological networksBiological networks

Gene-protein

GENOME

1010

Gene-protein interactions

Protein-protein interactions

PROTEOME

Citrate Cycle

METABOLISM

Biochemical reactions


Yeast protein interaction networkYeast protein interaction network

1111from

H.

Jeong e

t al N

atu

re 4

11, 41 (

2001)


Ecological networkEcological network: Trophic relationships in a food web.: Trophic relationships in a food web.

1212


Telecommunication networkTelecommunication network

1313


InternetInternet

1414


World Wide WebWorld Wide Web

1515


Social networkSocial network: Bibliographic network (coauthors): Bibliographic network (coauthors)

1616


Social networkSocial network: Bibliographic network (coauthors): Bibliographic network (coauthors)

1717


Social networkSocial network: FOAF (“friend of a friend”): FOAF (“friend of a friend”)

1818


Social networkSocial network: Organization: Organization

1919


Social networkSocial network: US Biotech Industry: US Biotech Industry

2020

Network PropertiesNetwork Properties

Common network features:Common network features:

�� Large scale.Large scale.

�� Continuous evolution.Continuous evolution.

�� Distribution (nodes decide their connections).Distribution (nodes decide their connections).

�� Interactions only through existing links.Interactions only through existing links.

2121


Some interesting structural properties:Some interesting structural properties:

�� Connected components: How many? Of what size?.Connected components: How many? Of what size?.

�� Network diameter: Average distance, worst case…Network diameter: Average distance, worst case…

�� Node degree distribution Node degree distribution & existence of “hubs” (heavily& existence of “hubs” (heavily--connected nodes).connected nodes).

�� Groupings (balance between local and largeGroupings (balance between local and large--distance distance connections, as well as their roles).connections, as well as their roles). 2222


Network ConnectivityNetwork Connectivity

WWWWWW

2323


Network DiameterNetwork Diameter

“small worlds”“small worlds”

Sarah

2424

Tim

Jane

Sarah

Ralph


Clustering coefficientClustering coefficient

nbr(u) nbr(u) Neighbors of the node u in the network.Neighbors of the node u in the network.

kk Number of neighbors of u, i.e. |nbr(u)|.Number of neighbors of u, i.e. |nbr(u)|.

max(u)max(u) Maximum number of links among the Maximum number of links among the max(u)max(u) Maximum number of links among the Maximum number of links among the neighbors of u, e.g. k*(kneighbors of u, e.g. k*(k--1)/2.1)/2.

Clustering coefficient for the node u:Clustering coefficient for the node u:c(u) = (#links among neighbors of u) / max(u)c(u) = (#links among neighbors of u) / max(u)

Clustering coefficient for the graph G:Clustering coefficient for the graph G:C = average of c(u) for every node in GC = average of c(u) for every node in G 2525


Clustering coefficientClustering coefficient

k = 4k = 4

m = 6m = 6

uc(u) = 4/6 = 0.66c(u) = 4/6 = 0.66

0 <= c(u) <= 10 <= c(u) <= 1

Similarity of u neighbors to a clique (complete graph).Similarity of u neighbors to a clique (complete graph).

Informal interpretation:Informal interpretation:

“My friends tend to be friends among them.”“My friends tend to be friends among them.”2626


Clustering coefficient Clustering coefficient for some real networksfor some real networks

Network N C Crand L

WWW 153127 0.1078 0.00023 3.1

Internet 3015-6209 0.18-0.30 0.001 3.7-3.76

Actor 225226 0.79 0.00027 3.65

Clustering coefficient (C):Clustering coefficient (C): C>CC>Crandrand

Path length (L): Path length (L): L<LL<Lrandrand2727

Actor 225226 0.79 0.00027 3.65

Coauthorship 52909 0.43 0.00018 5.9

Metabolic 282 0.32 0.026 2.9

Foodweb 134 0.22 0.06 2.43

C. elegance 282 0.28 0.05 2.65


Node degree distributionNode degree distribution

Normal distributionNormal distribution

Parameters: Average & deviationParameters: Average & deviation

2828



Poisson distributionPoisson distribution

Single parameter: Single parameter: λλ (mean (mean & deviation)& deviation)

2929



Pareto distribution (a.k.a. “power law”)Pareto distribution (a.k.a. “power law”)

Single parameter: Single parameter: αααααααα

P(x) P(x) ~ x~ x~ x~ x~ x~ x~ x~ x--------ααααααααP(x) P(x) ~ x~ x~ x~ x~ x~ x~ x~ x--------αααααααα

The Pareto principle (the “80The Pareto principle (the “80--20 rule”):20 rule”):

20% of the population controls 80% of the wealth.20% of the population controls 80% of the wealth.3030



HubsHubs

Small number of nodes with a very high degree.Small number of nodes with a very high degree.

�� Hubs appear with power laws (Hubs appear with power laws (P(x) P(x) ~ x~ x~ x~ x~ x~ x~ x~ x--------αααααααα),),but not with normal/binomial/Poisson distributions.but not with normal/binomial/Poisson distributions. 3131



LogLog--log plotlog plot

�� Pareto distribution Pareto distribution �� log(Pr[X = x]) = log(1/xlog(Pr[X = x]) = log(1/xαα) = ) = --αα log(x) log(x) log(Pr[X = x]) = log(1/xlog(Pr[X = x]) = log(1/x ) = ) = --αα log(x) log(x)

�� Linear, Linear, ––α α slope.slope.

�� Normal distributionNormal distribution�� log(Pr[X = x]) = log(a exp(log(Pr[X = x]) = log(a exp(--xx22/b)) = log(a) /b)) = log(a) –– xx22/b/b

�� Nonlinear, concave around the average.Nonlinear, concave around the average.

�� Poisson distributionPoisson distribution�� log(Pr[X = x]) = log(exp(log(Pr[X = x]) = log(exp(--λλ) ) λλxx/x!) /x!)

�� Nonlinear.Nonlinear. 3232



LogLog--log plotlog plot

aa WWWWWWpower lawpower law

bb Coauthorship networksCoauthorship networkspower law with exponential cutoffpower law with exponential cutoff

cc Power gridPower gridexponentialexponential

dd Social networkSocial networkGaussianGaussian

3333

Network ModelsNetwork Models

“Natural” networks tend to have…“Natural” networks tend to have…

�� One (or a few) connected components.One (or a few) connected components.�� Independent of network size.Independent of network size.

�� A small diameter (“six degrees of separation”).A small diameter (“six degrees of separation”).�� A small diameter (“six degrees of separation”).A small diameter (“six degrees of separation”).�� Constant, logarithmically increasing, Constant, logarithmically increasing,

or even decreasing with network size.or even decreasing with network size.

�� High clustering (“communities”).High clustering (“communities”).�� Much larger than expected from a random networkMuch larger than expected from a random network

(and, even so, with a small diameter!).(and, even so, with a small diameter!).

�� A mixture of connections.A mixture of connections.�� Local vs. “longLocal vs. “long--distance” connectionsdistance” connections

Do they share some “universal” features?Do they share some “universal” features? 3434


�� Random networks.Random networks.

�� RandomRandom--biased networks.biased networks.

�� SmallSmall--world networks.world networks.

�� ScaleScale--free networks.free networks.

�� Hierarchical & modular networks.Hierarchical & modular networks.

�� Affiliation networks.Affiliation networks.3535


Random NetworksRandom Networks

ErdösErdös--Rényi modelRényi model

�� Small number of connected components (typically one).Small number of connected components (typically one).

�� Low clustering coefficient.Low clustering coefficient.

�� Poisson distribution.Poisson distribution.�� Poisson distribution.Poisson distribution.

3636



ErdösErdös--Renyi modelRenyi model

Princi

pal co

mponent

3737

Number of links

Princi

pal co

mponent



Example: Romantic relationships in the Add Health data set.Example: Romantic relationships in the Add Health data set.

Peter S. Bearman, James Moody & Katherine Stovel:Peter S. Bearman, James Moody & Katherine Stovel:

“Chains of Affection: The Structure of Adolescent Romantic and Sexual Networks”“Chains of Affection: The Structure of Adolescent Romantic and Sexual Networks”

American Journal of Sociology, 110(1):44American Journal of Sociology, 110(1):44––91, July 200491, July 2004

3838


SmallSmall--World NetworksWorld Networks

Watts & Strogatz modelWatts & Strogatz model


�� Small diameter.Small diameter.

�� Poisson distribution.Poisson distribution.�� Poisson distribution.Poisson distribution.

�� High clustering coefficient.High clustering coefficient.

3939


SmallSmall--World NetworksWorld Networks

Watts & Strogatz modelWatts & Strogatz model

Average path length, normalized by system size, Average path length, normalized by system size, plotted as a function of the average number of shortcuts.plotted as a function of the average number of shortcuts. 4040


ScaleScale--Free NetworksFree Networks

Barabási & Albert modelBarabási & Albert model


�� Small diameter.Small diameter.

�� Pareto distribution.Pareto distribution.�� Pareto distribution.Pareto distribution.

�� Small clustering coefficient.Small clustering coefficient.

�� Hubs.Hubs.

4141




“Natural” interpretation of the model:

�� Variable number of nodes: Variable number of nodes: Network grows as new nodes are added.Network grows as new nodes are added.

�� Preferential attachmentPreferential attachment::The more connected a node is, The more connected a node is, the more likely it is to receive new linksthe more likely it is to receive new links(“rich get richer” or Matthew effect).(“rich get richer” or Matthew effect).

4242




Exponential model… Scale-free model…

… without hubs. … with hubs. 4343


PoissonPoisson Pareto (power law)Pareto (power law)

4444



FeaturesFeatures

�� SelfSelf--organization traits: Links are not randomorganization traits: Links are not random(a feature found in many complex systems).(a feature found in many complex systems).(a feature found in many complex systems).(a feature found in many complex systems).

�� Tolerance to random attacks, which easily disrupt Tolerance to random attacks, which easily disrupt random networks but not scalerandom networks but not scale--free networks.free networks.

�� Vulnerability to targeted attacks: Vulnerability to targeted attacks: “Hubs” are essential to maintain connectedness.“Hubs” are essential to maintain connectedness.

4545


4646


Hierarchical/Modular NetworksHierarchical/Modular Networks

�� Hierarchical organization.Hierarchical organization.

�� Hubs.Hubs.

�� CliquesCliques..

4747


Hierarchical/Modular NetworksHierarchical/Modular Networks

4848


Affiliation NetworksAffiliation Networks

Bipartite graph to model social interactionsBipartite graph to model social interactions::

4949


Affiliation NetworksAffiliation Networks

5050


5151

Network Structure & DynamicsNetwork Structure & Dynamics

The countless ways in which network structuresThe countless ways in which network structuresaffect our lives make it critical to understand:affect our lives make it critical to understand:

1.1. How network structures affect behavior.How network structures affect behavior.

2.2. Which network structures are likely to emerge.Which network structures are likely to emerge.

5252


A complex system is a system composed of A complex system is a system composed of interconnected parts that, as a whole, exhibit one or interconnected parts that, as a whole, exhibit one or interconnected parts that, as a whole, exhibit one or interconnected parts that, as a whole, exhibit one or more properties (behavior) not obvious from the more properties (behavior) not obvious from the properties of the individual parts (i.e. emergence).properties of the individual parts (i.e. emergence).

5353


Research problemsResearch problems

�� Search on networks Search on networks (with partial local information)(with partial local information)

�� Diffusion problems:Diffusion problems:epidemics, social contagion (ideas, fads, products…)epidemics, social contagion (ideas, fads, products…)

�� Analysis of network propertiesAnalysis of network propertiese.g. robustness/vulnerabilitye.g. robustness/vulnerability

5454


From an algorithmic point of view…From an algorithmic point of view…

�� Objects: Objects: �� Ranking (HITS, PageRank…).Ranking (HITS, PageRank…).

�� Classification & anomaly detection.Classification & anomaly detection.

Clustering & community analysis.Clustering & community analysis.�� Clustering & community analysis.Clustering & community analysis.

�� Object identification (e.g. “entity resolution”).Object identification (e.g. “entity resolution”).

�� Links:Links:�� Link prediction.Link prediction.

�� Graphs:Graphs:�� Subgraph detection.Subgraph detection.

�� Graph classification.Graph classification.

�� Graph generation models.Graph generation models.

�� …… 5555

BibliographyBibliography

Networks: Origins & Applications (social networks, Web…)Networks: Origins & Applications (social networks, Web…)�� Stanley Milgram: Stanley Milgram: The small world problemThe small world problem. .

Psychology Today, 2:60Psychology Today, 2:60--67 (1967)67 (1967)

�� Phillip W. Anderson: Phillip W. Anderson: More is differentMore is different..Science, 177:393Science, 177:393--396 (1972)396 (1972)

�� Mark S. Granovetter: Mark S. Granovetter: The strength of weak tiesThe strength of weak ties..American Journal of Sociology, 78:1360American Journal of Sociology, 78:1360--1380 (1973)1380 (1973)

�� Stanley Wasserman & Katherine Faust: Stanley Wasserman & Katherine Faust: Social Network Analysis: Methods and Social Network Analysis: Methods and �� Stanley Wasserman & Katherine Faust: Stanley Wasserman & Katherine Faust: Social Network Analysis: Methods and Social Network Analysis: Methods and ApplicationsApplications. Cambridge University Press, 1994. Cambridge University Press, 1994

�� John P. Scott: John P. Scott: Social Network AnalysisSocial Network Analysis, 2nd edition., 2nd edition.Sage Publications Ltd., 2000. Sage Publications Ltd., 2000.

�� Andrei Broder, Ravi Kumar, Farzin Maghoul, Prabhakar Raghavan, Sridhar Rajagopalan, Andrei Broder, Ravi Kumar, Farzin Maghoul, Prabhakar Raghavan, Sridhar Rajagopalan, Raymie Stata, Andrew Tomkins & Janet Wiener: Raymie Stata, Andrew Tomkins & Janet Wiener: Graph structure in the WebGraph structure in the Web. Computer . Computer Networks 33:309Networks 33:309––320 (2000)320 (2000)

�� Steven H. Strogatz: Steven H. Strogatz: Exploring Complex NetworksExploring Complex Networks..Nature, 410:268Nature, 410:268--275 (2001)275 (2001)

�� AlbertAlbert--Laszlo Barabasi: Laszlo Barabasi: Linked: How Everything Is Connected to Everything Else and Linked: How Everything Is Connected to Everything Else and What It MeansWhat It Means. Plume, 2003. ISBN 0452284392. Plume, 2003. ISBN 0452284392

�� Duncan J. Watts: Duncan J. Watts: Six Degrees: The Science of a Connected AgeSix Degrees: The Science of a Connected Age. W. W. Norton & . W. W. Norton & Company, 2004. ISBN 0393325423Company, 2004. ISBN 0393325423

�� Jure Leskovec, Jon M. Kleinberg & Christos Faloutsos: Jure Leskovec, Jon M. Kleinberg & Christos Faloutsos: Graphs over time: densification Graphs over time: densification laws, shrinking diameters and possible explanationslaws, shrinking diameters and possible explanations. KDD'2005. KDD'2005

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Network ModelsNetwork Models�� Paul ErdPaul Erdöös & Alfred Rs & Alfred Réényi: nyi: On the evolution of random graphsOn the evolution of random graphs..

Mathematical Institute of the Hungarian Academy of Sciences, 5:17Mathematical Institute of the Hungarian Academy of Sciences, 5:17--61 (1960) 61 (1960) reprinted in Duncan, Barabasi & Watts (eds.): reprinted in Duncan, Barabasi & Watts (eds.): ““The Structure and Dynamics of NetworksThe Structure and Dynamics of Networks””

�� Ray Solomonoff & Anatol Rapoport: Ray Solomonoff & Anatol Rapoport: Connectivity of random netsConnectivity of random nets..Bulletin of Mathematical Biophysics, 13:107Bulletin of Mathematical Biophysics, 13:107--117 (1951)117 (1951)reprinted in Duncan, Barabasi & Watts (eds.): reprinted in Duncan, Barabasi & Watts (eds.): ““The Structure and Dynamics of NetworksThe Structure and Dynamics of Networks””

�� Duncan J. Watts & Steven H. Strogatz: Duncan J. Watts & Steven H. Strogatz: Collective dynamics of Collective dynamics of ‘‘smallsmall--worldworld’’ networksnetworks..�� Duncan J. Watts & Steven H. Strogatz: Duncan J. Watts & Steven H. Strogatz: Collective dynamics of Collective dynamics of ‘‘smallsmall--worldworld’’ networksnetworks..Nature, 393:440Nature, 393:440--442 (1998)442 (1998)

�� AlbertAlbert--LLáászlszlóó BarabBarabáási & Rsi & Rééka Albert: ka Albert: Emergence of scaling in random networksEmergence of scaling in random networks..Science, 286:509Science, 286:509--512 (1999)512 (1999)

�� RRééka Albert, Hawoong Jeong & Albertka Albert, Hawoong Jeong & Albert--LLáászlszlóó BarabBarabáási: si: Error and attack tolerance of Error and attack tolerance of

complex networkscomplex networks. Nature 406:378. Nature 406:378--382 (2000)382 (2000)

�� M.E.J. Newman, S.H. Strogatz & D.J. Watts: M.E.J. Newman, S.H. Strogatz & D.J. Watts: Random graphs with arbitrary degree Random graphs with arbitrary degree distributions and their applicationsdistributions and their applications. Physical Review E, 64:026118 (2001). Physical Review E, 64:026118 (2001)

�� M.E.J. Newman, S.H. Strogatz & D.J. Watts: M.E.J. Newman, S.H. Strogatz & D.J. Watts: Random graphs models of social networksRandom graphs models of social networks. . PNAS 99:2566PNAS 99:2566--2572 (2002)2572 (2002)

�� ErzsErzséébet Ravasz & Albertbet Ravasz & Albert--LLáászlszlóó BarabBarabáási: si: Hierarchical organization in complex Hierarchical organization in complex

networksnetworks. Physical Review E, 67:026112 (2003). Physical Review E, 67:026112 (2003)

�� Mark Newman: Mark Newman: The structure and function of complex networksThe structure and function of complex networks. SIAM Review . SIAM Review 45:16745:167--256 (2003)256 (2003) 5757


Search on NetworksSearch on Networks�� Sergey Brin & Lawrence Page: Sergey Brin & Lawrence Page: The anatomy of a largeThe anatomy of a large--scale hypertextual Web search scale hypertextual Web search

engineengine. Computer Networks and ISDN Systems, April 1998. Computer Networks and ISDN Systems, April 1998

�� David Gibson, Jon M. Kleinberg & Prabhakar Raghavan: David Gibson, Jon M. Kleinberg & Prabhakar Raghavan: Inferring Web Communities from Inferring Web Communities from Link TopologyLink Topology. ACM Conference on Hypertext and Hypermedia, June 1998. ACM Conference on Hypertext and Hypermedia, June 1998

�� Jon M. Kleinberg: Jon M. Kleinberg: Authoritative sources in a hyperlinked environmentAuthoritative sources in a hyperlinked environment. . Journal of the ACM, September 1999Journal of the ACM, September 1999

�� Toby Walsh: Toby Walsh: Search in a Small WorldSearch in a Small World. IJCAI. IJCAI’’19991999�� Toby Walsh: Toby Walsh: Search in a Small WorldSearch in a Small World. IJCAI. IJCAI’’19991999

�� Jon M. Kleinberg. Jon M. Kleinberg. Navigation in a Small WorldNavigation in a Small World. Nature, August 2000.. Nature, August 2000.

�� Jon M. Kleinberg: Jon M. Kleinberg: The smallThe small--world phenomenon: An algorithm perspectiveworld phenomenon: An algorithm perspective. . STOCSTOC’’2000 2000

�� Scott White & Scott White & PadhraicPadhraic Smyth: Smyth: Algorithms for Estimating Relative Importance in Algorithms for Estimating Relative Importance in NetworksNetworks. KDD'2003. KDD'2003

�� HanghangHanghang Tong & Christos Tong & Christos FaloutsosFaloutsos: : CenterCenter--Piece Piece SubgraphsSubgraphs: Problem Definition and : Problem Definition and Fast SolutionsFast Solutions. KDD'2006. KDD'2006

�� AlekhAlekh AgarwalAgarwal, , SoumenSoumen ChakrabartiChakrabarti & Sunny & Sunny AggarwalAggarwal: : Learning to Rank Networked Learning to Rank Networked EntitiesEntities. KDD'2006. KDD'2006

�� Jeffrey Jeffrey DavitzDavitz, , JiyeJiye Yu, Yu, SugatoSugato BasuBasu, David , David GuteliusGutelius & Alexandra Harris: & Alexandra Harris: iLinkiLink: Search and : Search and Routing in Social NetworksRouting in Social Networks. KDD'2007. . KDD'2007.

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�� Mark Newman, AlbertMark Newman, Albert--Laszlo Laszlo BarabasiBarabasi & Duncan J. Watts & Duncan J. Watts (editors): (editors): The Structure and Dynamics of NetworksThe Structure and Dynamics of Networks. . Princeton University Press, 2006. ISBN 0Princeton University Press, 2006. ISBN 0--691691--1135711357--22

�� Ted G. Lewis: Ted G. Lewis: Network Science: Theory and ApplicationsNetwork Science: Theory and Applications..Wiley, 2009. ISBN 0Wiley, 2009. ISBN 0--470470--3318833188--7 7

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�� David Easley & Jon Kleinberg: David Easley & Jon Kleinberg: Networks, Crowds, and Networks, Crowds, and Markets: Reasoning About a Highly Connected WorldMarkets: Reasoning About a Highly Connected World. . Cambridge University Press, 2010. ISBN Cambridge University Press, 2010. ISBN 05211953300521195330http://www.cs.cornell.edu/home/kleinber/networkshttp://www.cs.cornell.edu/home/kleinber/networks--book/book/

�� Mark Newman: Mark Newman: Networks: An IntroductionNetworks: An Introduction. . Oxford University Press, 2010. ISBN Oxford University Press, 2010. ISBN 00--1919--920665920665--11

�� Matthew O. Jackson: Matthew O. Jackson: Social and Economic NetworksSocial and Economic Networks, , Princeton University Press, 2008. ISBN Princeton University Press, 2008. ISBN 00--691691--1344013440--55

6060


�� AlbertAlbert--Laszlo Barabási: Laszlo Barabási: Linked: How Everything Is Linked: How Everything Is Connected to Everything Else and What It MeansConnected to Everything Else and What It Means. . Plume, 2003. ISBN 0452284392Plume, 2003. ISBN 0452284392

�� Duncan J. Watts: Duncan J. Watts: Six Degrees: The Science of a Connected Six Degrees: The Science of a Connected AgeAge. W. W. Norton & Company, 2004. ISBN 0393325423. W. W. Norton & Company, 2004. ISBN 0393325423

�� AlbertAlbert--Laszlo Barabási: Laszlo Barabási: Bursts: The Hidden Pattern Behind Bursts: The Hidden Pattern Behind �� AlbertAlbert--Laszlo Barabási: Laszlo Barabási: Bursts: The Hidden Pattern Behind Bursts: The Hidden Pattern Behind Everything We DoEverything We Do. Dutton, 2010. ISBN . Dutton, 2010. ISBN 05259516010525951601

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mining complex data - networks - ugrelvex.ugr.es/decsai/intelligent/slides/dm/d6 networks.pdf ·...

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