Skip to main content
SpringerLink
Log in

Context-sensitive detection of local community structure

  • Original Article
  • Published:
Social Network Analysis and Mining Aims and scope Submit manuscript

Abstract

Local methods for detecting community structure are necessary when a graph’s size or node-expansion cost make global community detection methods infeasible. Various algorithms for local community detection have been proposed, but there has been little analysis of the circumstances under which one approach is preferable to another. This paper describes an evaluation comparing the accuracy of five alternative vertex selection policies in detecting two distinct types of community structures—vertex partitions that maximize modularity, and link partitions that maximize partition density—in a variety of graphs. In this evaluation, the vertex selection policy that most accurately identified vertex-partition community structure in a given graph depended on how closely the graph’s degree distribution approximated a power-law distribution. When the target community structure was partition-density maximization, however, an algorithm based on spreading activation generally performed best, regardless of degree distribution. These results indicate that local community detection should be context-sensitive in the sense of basing vertex selection on the graph’s degree distribution and the target community structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. The algorithm of Luo et al. (2008) considers each \(n \in N\) in ascending order of degree, adding to the community each n whose addition to C would increase M. Each element of C whose removal would increase M without disconnecting C is then removed. These two steps are repeated until no new vertices are added. The procedure described here differs from the algorithm of Luo et al. (2008) in that it selects the node that maximizes M, rather than the lowest degree node for which \(\Updelta M>O,\) and in that it is purely a node-selection policy, with no node filtering.

  2. An alternative approach to spreading activation based on the Katz (1953) index assigns activation to node \(n \in N \hbox{ equal to} =\sum\nolimits_{l=1}^{\infty}\delta^l \cdot |\{ w_l(q,n)\}|,\) where {w l (q, n)} is the set of all walks of length l from query vertex q to vertex n and δ is an attenuation factor. This approach exhibited behavior very similar to that of MaxActivation in the evaluation set forth below but for brevity is omitted.

  3. For a discussion of alternatives to the GN benchmarks, see Lancichinetti et al. (2008).

  4. Clauset et al. (2009) describe a procedure for fitting degree distributions to a power-law function and provide code for this procedure at http://www.santafe.edu/~aaronc/powerlaws. Under this procedure, none of the 12 graphs has a statistically significant fit to a power-law distribution.

  5. The highest modularity partition of a graph does not necessarily correspond to the actual community structure (Fortunato and Barthelemy 2007), and alternative metrics sometimes lead to better community structure (Rosvall and Bergstrom 2007; Branting 2010b; Koutsourelakis and Eliassi-Rad 2008). However, modularity is the best-known community-structure criterion, so for reproducibility of the results described here, the partition that globally optimizes modularity was chosen as the first target community structure.

  6. For link-partition communities, k was the size of the largest community containing s.

References

  • Ahn Y-Y, Bagrow JP (2010) Link communities reveal multiscale complexity in networks. Nature 466(7307):761–764

    Article  Google Scholar 

  • Bagrow J (2008) Evaluating local community methods in networks. J Stat Mech 2008(5):P05001

    Article  Google Scholar 

  • Bagrow J, Bollt E (2005) Local method for detecting communities. Phys Rev E 72(4):046108

    Article  Google Scholar 

  • Branting LK (2010a) Incremental detection of local community structure. In: International conference on advances, in social network analysis and mining. IEEE Computer Society, Los Alamitos, CA, USA, pp 80–87

  • Branting LK (2010b) Information theoretic criteria for community detection. Adv Soc Netw Min Anal Lect Notes Comput Sci 5498:114–130

    Article  Google Scholar 

  • Baeza-Yates R, Ribeiro-Neto B (1999) Modern information retrieval. Addison-Wesley, Reading

    Google Scholar 

  • Chakrabarti D (2004) Autopart: parameter-free graph partitioning and outlier detection. In: Proceedings of the European conference on machine learning and practice of knowledge discovery in databases, pp 112–124

  • Chen J, Zaiane O, Goebel R (2009) Local community identification in social networks. In: Proceedings of the international conference on advances in social networks analysis and mining (ASONAM), Athens, Greece, 20–22 July

  • Clauset A (2005) Finding local community structure in networks. Phys Rev E (Stat Nonlinear Soft Matter Phys) 72(2):026132 (online). http://link.aps.org/abstract/PRE/v72/e026132

  • Clauset A, Shalizi C, Newman M (2009) Power-law distributions in empirical data. SIAM Rev 51(4):661–703

    Article  MathSciNet  MATH  Google Scholar 

  • Cohen J (2008) Barycentric graph clustering. http://www2.computer.org/cms/Computer.org/dl/mags/cs/2009/04/extras/msp2009040029s2.pdf

  • Collins A, Loftus F (1975) A spreading-activation theory of semantic processing. Psychol Rev 82(6):407–428

    Article  Google Scholar 

  • Crestani F (1997) Application of spreading activation techniques in information retrieval. Artif Intell Rev 11(6):453–482

    Article  Google Scholar 

  • Danon L, Díaz-Guilera A, Duch J, Arenas A (2005) Comparing community structure identification. J Stat Mech Theory Exp 2005(9):P09008 (online). http://stacks.iop.org/1742-5468/2005/i=09/a=P09008

  • Fortunato S, Barthelemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci 104(1):36–41

    Article  Google Scholar 

  • Girvan M, Newman M (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99(12):7821–7826

    Article  MathSciNet  MATH  Google Scholar 

  • Gleiser PM, Danon L (2003) Community structure in jazz. Adv Complex Syst (ACS) 6(4):565–573

    Article  Google Scholar 

  • Jin D, He D, Liu D, Baquero C (2010) Genetic algorithm with local search for community mining in complex networks. In: ICTAI (1)’10, pp 105–112

  • Katz L (1953) A new status index derived from sociometric analysis. Psychometrika 18(1):39–43

    Article  MATH  Google Scholar 

  • Koutsourelakis P, Eliassi-Rad T (2008) Finding mixed-memberships in social networks. In: Proceedings of the 2008 AAAI spring symposium on social information processing. AAAI, Stanford, CA

  • Knuth D (1993) The Stanford GraphBase: a platform for combinatorial computing. ACM, New York

    Google Scholar 

  • Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys Rev E 78:046110

    Article  Google Scholar 

  • Leskovec J, Lang K, Mahoney M (2010) Empirical comparison of algorithms for network community detection. In: Proceedings of the international conference on World Wide Web (WWW), 26–30 April. ACM, Raleigh, NC

  • Luo F, Wang J, Promislow E (2008) Exploring local community structures in large networks. Web Intell Agent Syst 6(4):387–400

    Google Scholar 

  • Lusseau D, Schneider K, Boisseau O, Haase P, Slooten E, Dawson S (2003) The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behav Ecol Sociobiol 54(4):396–405

    Article  Google Scholar 

  • Muff ACS, Rao F (2005) Local modularity measure for network clusterizations. Phys Rev E 72:056107

    Article  Google Scholar 

  • Newman MEJ (2004) Fast algorithm for detecting community structure in networks. Phys Rev E 69:066133 (online). doi:10.1103/PhysRevE.69.066133

    Google Scholar 

  • Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E (Stat Nonlinear Soft Matter Phys) 74(3):036104+ (online). http://dx.doi.org/10.1103/PhysRevE.74.036104

  • Newman M (2009) Network data. http://www-personal.umich.edu/~mejn/netdata/

  • Newman ME, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E Stat Nonlinear Soft Matter Phys 69(2 Pt 2):026113 (online). http://view.ncbi.nlm.nih.gov/pubmed/14995526

  • Raghavan UN, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E 76:036106

    Article  Google Scholar 

  • Rosvall M, Bergstrom C (2007) An information-theoretic framework for resolving community structure in complex networks. Proc Natl Acad Sci USA 104:7327–7331

    Article  Google Scholar 

  • Rosvall M, Bergstrom CT (2008) Maps of random walks on complex networks reveal community structure. Proc Natl Acad Sci USA 105(4):1118–1123

    Article  Google Scholar 

  • Watts D, Strogatz S (1998) Collective dynamics of ’small-world’ networks. Nature 393(6684):440–442

    Article  Google Scholar 

  • Zachary W (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33:452–473

    Google Scholar 

  • Zhang H, Giles CL, Foley HC, Yen J (2007) Probabilistic community discovery using hierarchical latent gaussian mixture model. In: AAAI’07: proceedings of the 22nd national conference on artificial intelligence. AAAI Press, Menlo Park, pp 663–668

Download references

Acknowledgments

This work was funded under contract number CECOM W15P7T-09-C-F600. The MITRE Corporation is a not-for-profit Federally Funded Research and Development Center chartered in the public interest.

Author information

Authors and Affiliations

  1. The MITRE Corporation, 7525 Colshire Drive, McLean, VA, USA

    L. Karl Branting

Authors
  1. L. Karl Branting
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Karl Branting.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Branting, L.K. Context-sensitive detection of local community structure. Soc. Netw. Anal. Min. 2, 279–289 (2012). https://doi.org/10.1007/s13278-011-0035-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13278-011-0035-7

Keywords

Search

Navigation