Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Game-Theoretic Framework for Community Detection

  • Patrick J. McSweeney
  • Kishan Mehrotra
  • Jae C. Oh
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_350

Synonyms

Glossary

CDG

Community detection game

LFR

A model of games with built-in community structure

Network Structure

An abstraction of how groups of individuals interact with each other

NMI

Normalized mutual information

Social Network

A network made up of a set of individuals or organizations and ties (edges) between the individuals

The Resolution Limit

The limitations in detecting small community structures in a large network

Introduction

“Communities” constitute an important aspect of networks, and studying their formation and dynamics is essential. Graphs without communities, e.g., those in which any edge may exist with the same probability, are interesting objects for mathematical study but are rarely mirrored in real life. A rough analogy is the distribution of matter in the universe: if it had been uniform, with no galaxies, stars, or planets, it would be far less interesting than our current universe....

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References

  1. Adamic LA, Glance N (2005) The political blogosphere and the 2004 US election: divided they blog. In: LinkKDD ‘05: proceedings of the 3rd international workshop on link discovery, Chicago. ACM, New York, pp 36–43Google Scholar
  2. Batagelj V, Mrvar A (1998) Program for large network analysis. Connect 21:47–57Google Scholar
  3. Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech 2008:P10008CrossRefGoogle Scholar
  4. Bogomolnaia A, Jackson MO (2002) The stability of hedonic coalition structures. Games Econ Behav 38(2):201–230MathSciNetMATHCrossRefGoogle Scholar
  5. Danon L, Diaz-Guilera A, Duch J, Arenas A (2005) Comparing community structure identification. J Stat Mech Theory Exp 2005(09):P09008CrossRefGoogle Scholar
  6. Duch J, Arenas A (2005) Community detection in complex networks using extremal optimization. Phys Rev E 72:027104CrossRefGoogle Scholar
  7. Fortunato S (2007) Quality functions in community detection. In: Proceedings of SPIE international conference “fluctuations and noise 2007”, FlorenceGoogle Scholar
  8. Fortunato S, Barthelemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci U S A 104:36CrossRefGoogle Scholar
  9. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci U S A 99:7821.  https://doi.org/10.1073/pnas.122653799MathSciNetCrossRefMATHGoogle Scholar
  10. Good BH, de Montjoye YA, Clauset A (2010) The performance of modularity maximization in practical contexts. Phys Rev E 81:046106MathSciNetCrossRefGoogle Scholar
  11. Gunes I, Bingol H (2009) Community detection in complex networks using agents. In: Discovery science, PortoGoogle Scholar
  12. Heimo T, Kumpula J, Kaski K, Saramaki J (2008) Detecting modules in dense weighted networks with the Potts method. J Stat Mech Theory Exp 2008:08007CrossRefGoogle Scholar
  13. Kolaczyk ED (2009) Statistical analysis of network data: methods and models. Springer, New York/LondonMATHCrossRefGoogle Scholar
  14. Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys Rev E 78:046110CrossRefGoogle Scholar
  15. Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298(5594):824–827CrossRefGoogle Scholar
  16. Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74(3):036104.  https://doi.org/10.1103/PhysRevE.74.036104MathSciNetCrossRefGoogle Scholar
  17. Newman MEJ (2010) Networks: an introduction. Oxford University Press, Oxford/New YorkMATHCrossRefGoogle Scholar
  18. Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69:026113.  https://doi.org/10.1103/PhysRevE.69.026113CrossRefGoogle Scholar
  19. Shapley L (1953) A value for n-person games. In: Kuhn H, Tucker AW (eds) Contributions to the theory of games (II). Annals of mathematics studies, vol 28. Princeton University Press, Princeton, pp 307–317Google Scholar
  20. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440–442MATHCrossRefGoogle Scholar
  21. Zachary WW (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33:452–473CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  • Patrick J. McSweeney
    • 1
  • Kishan Mehrotra
    • 1
  • Jae C. Oh
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceSyracuse UniversitySyracuseUSA

Section editors and affiliations

  • Fakhreddine Karray
    • 1
  1. 1.Department of Electrical and Computer Engineering, Centre for Pattern Analysis and Machine Intelligence (CPAMI)University of WaterlooWaterlooCanada