Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T16:04:56.854Z Has data issue: false hasContentIssue false
  • English
  • Français

Relative centrality and local community detection

Published online by Cambridge University Press:  17 August 2015

CHENG-SHANG CHANG ,
CHIH-JUNG CHANG ,
WEN-TING HSIEH ,
DUAN-SHIN LEE ,
LI-HENG LIOU  and
WANJIUN LIAO
CHENG-SHANG CHANG
Affiliation:
Institute of Communications Engineering, National Tsing Hua University, Hsinchu 300, Taiwan, Republic of China (e-mail: cschang@ee.nthu.edu.tw, u9661234@oz.nthu.edu.tw, athena41393@livemail.tw, dacapo1142@gmail.com, lds@cs.nthu.edu.tw)
CHIH-JUNG CHANG
Affiliation:
Institute of Communications Engineering, National Tsing Hua University, Hsinchu 300, Taiwan, Republic of China (e-mail: cschang@ee.nthu.edu.tw, u9661234@oz.nthu.edu.tw, athena41393@livemail.tw, dacapo1142@gmail.com, lds@cs.nthu.edu.tw)
WEN-TING HSIEH
Affiliation:
Institute of Communications Engineering, National Tsing Hua University, Hsinchu 300, Taiwan, Republic of China (e-mail: cschang@ee.nthu.edu.tw, u9661234@oz.nthu.edu.tw, athena41393@livemail.tw, dacapo1142@gmail.com, lds@cs.nthu.edu.tw)
DUAN-SHIN LEE
Affiliation:
Institute of Communications Engineering, National Tsing Hua University, Hsinchu 300, Taiwan, Republic of China (e-mail: cschang@ee.nthu.edu.tw, u9661234@oz.nthu.edu.tw, athena41393@livemail.tw, dacapo1142@gmail.com, lds@cs.nthu.edu.tw)
LI-HENG LIOU
Affiliation:
Institute of Communications Engineering, National Tsing Hua University, Hsinchu 300, Taiwan, Republic of China (e-mail: cschang@ee.nthu.edu.tw, u9661234@oz.nthu.edu.tw, athena41393@livemail.tw, dacapo1142@gmail.com, lds@cs.nthu.edu.tw)
WANJIUN LIAO
Affiliation:
Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, Republic of China (e-mail: wjliao@ntu.edu.tw)
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we develop a formal framework for what a good community should look like and how strong a community is (community strength). One of the key innovations is to incorporate the concept of relative centrality into structural analysis of networks. In our framework, relative centrality is a measure that measures how important a set of nodes in a network is with respect to another set of nodes, and it is a generalization of centrality. Building on top of relative centrality, the community strength for a set of nodes is measured by the difference between its relative centrality with respect to itself and its centrality. A community is then a set of nodes with a nonnegative community strength. We show that our community strength is related to conductance that is commonly used for measuring the strength of a small community. We define the modularity for a partition of a network as the average community strength for a randomly selected node. Such a definition generalizes the original Newman's modularity and recovers the stability in as special cases. For the local community detection problem, we also develop efficient agglomerative algorithms that guarantee the community strength of the detected local community.

Keywords

network sciencelocal community detectioncentralitymodularityclustering algorithms
Type
Research Article
Information
Network Science , Volume 3 , Issue 4 , December 2015 , pp. 445 - 479
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andersen, R., Chung, F., & Lang, K. (2006). Local graph partitioning using pagerank vectors. In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, 2006. focs'06. IEEE pp. 475–486.CrossRefGoogle Scholar
Andersen, R., & Lang, K. J. (2006). Communities from seed sets. In Proceedings of the 15th International Conference on World Wide Web. ACM, pp. 223–232.Google Scholar
Arenas, A., Fernandez, A., & Gomez, S. (2008). Analysis of the structure of complex networks at different resolution levels. New Journal of Physics, 10 (5), 053039.CrossRefGoogle Scholar
Bell, J. R. (2012). Relative centrality measures. Retrieved from http://www.westpoint.edu/nsc/SiteAssets/SitePages/Publications Google Scholar
Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008 (10), P10008.Google Scholar
Boyd, S., Ghosh, A., Prabhakar, B., & Shah, D. (2005). Gossip algorithms: Design, analysis and applications. In Proceedings of the IEEE Infocom 2005. 24th Annual Joint Conference of the IEEE Computer and Communications Societies, vol. 3. IEEE, pp. 1653–1664.Google Scholar
Brandes, U., Robins, G., Mccranie, A., & Wasserman, S. (2013). What is network science? Network science, 1 (1), 1–15.Google Scholar
Chang, C.-S., Hsu, C.-Y., Cheng, J., & Lee, D.-S. (2011). A general probabilistic framework for detecting community structure in networks. In Proceedings IEEE Infocom, 2011. IEEE, pp. 730–738.CrossRefGoogle Scholar
Clauset, A. (2005). Finding local community structure in networks. Physical Review E, 72 (2), 026132.Google Scholar
Clauset, A., Newman, M. E. J., & Moore, C. (2004). Finding community structure in very large networks. Physical Review E, 70 (6), 066111.Google Scholar
Csardi, G., & Nepusz, T. (2006). The igraph software package for complex network research. Interjournal, Complex Systems, 1695.Google Scholar
Danon, L., Diaz-Guilera, A., Duch, J., & Arenas, A. (2005). Comparing community structure identification. Journal of Statistical Mechanics: Theory and Experiment, 2005 (09), P09008.Google Scholar
Delvenne, J.-C., Yaliraki, S. N., & Barahona, M. (2010). Stability of graph communities across time scales. Proceedings of the National Academy of Sciences, 107 (29), 12755–12760.CrossRefGoogle ScholarPubMed
Dhillon, I. S., Guan, Y., & Kulis, B. (2004). Kernel k-means: Spectral clustering and normalized cuts. In Proceedings of the 10th acm sigkdd International Conference on Knowledge Discovery and Data Mining. ACM, pp. 551–556.Google Scholar
Diaconis, P., & Stroock, D. (1991). Geometric bounds for eigenvalues of markov chains. The Annals of Applied Probability, 1 (1), 36–61.Google Scholar
Duch, J., & Arenas, A. (2005). Community detection in complex networks using extremal optimization. Physical Review E, 72 (2), 027104.Google Scholar
Fortunato, S. (2010). Community detection in graphs. Physics Reports, 486 (3), 75–174.Google Scholar
Fortunato, S., & Barthelemy, M. (2007). Resolution limit in community detection. Proceedings of the National Academy of Sciences, 104 (1), 36–41.Google Scholar
Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40 (1), 35–41.Google Scholar
Freeman, L. C. (1979). Centrality in social networks conceptual clarification. Social Networks, 1 (3), 215–239.CrossRefGoogle Scholar
Girvan, M., & Newman, M. E. J. (2002). Community structure in social and biological networks. Proceedings of the National Academy of Sciences, 99 (12), 7821–7826.CrossRefGoogle ScholarPubMed
Granell, C., Gomez, S., & Arenas, A. (2012). Hierarchical multiresolution method to overcome the resolution limit in complex networks. International Journal of Bifurcation and Chaos, 22 (07), 1250171.Google Scholar
Hu, Y., Chen, H., Zhang, P., Li, M., Di, Z., & Fan, Y. (2008). Comparative definition of community and corresponding identifying algorithm. Physical Review E, 78 (2), 026121.Google Scholar
Huang, X.-C., Cheng, J., Chou, H.-H., Cheng, C.-H., & Chen, H.-T. (2013). Detecting overlapping communities in networks based on a simple node bahavior model. In Proceedings of IEEE Globecom 2013, pp. 3120–3125.Google Scholar
Kamvar, D. S., Klein, D., & Manning, C. (2003). Spectral learning. International Joint Conference of Artificial Intelligence. Stanford InfoLab.Google Scholar
Karrer, B., & Newman, M. E. J. (2011). Stochastic block models and community structure in networks. Physical Review E, 83 (1), 016107.Google Scholar
Karrer, B., Levina, E., & Newman, M. E. J. (2008). Robustness of community structure in networks. Physical Review E, 77 (4), 046119.CrossRefGoogle ScholarPubMed
Katz, L. (1953). A new status index derived from sociometric analysis. Psychometrika, 18 (1), 39–43.Google Scholar
Kulis, B., Basu, S., Dhillon, I., & Mooney, R. (2009). Semi-supervised graph clustering: A kernel approach. Machine Learning, 74 (1), 1–22.Google Scholar
Lambiotte, R. (2010). Multi-scale modularity in complex networks. In Proceedings of the 8th International Symposium on Modeling and Optimization in Mobile, ad hoc and Wireless Networks (wiopt). IEEE, pp. 546–553.Google Scholar
Lancichinetti, A., & Fortunato, S. (2009). Community detection algorithms: A comparative analysis. Physical Review E, 80 (5), 056117.Google Scholar
Lancichinetti, A., & Fortunato, S. (2011). Limits of modularity maximization in community detection. Physical Review E, 84 (6), 066122.Google Scholar
Lancichinetti, A., Fortunato, S., & Kertész, J. (2009). Detecting the overlapping and hierarchical community structure in complex networks. New Journal of Physics, 11 (3), 033015.Google Scholar
Lancichinetti, A., Fortunato, S., & Radicchi, F. (2008). Benchmark graphs for testing community detection algorithms. Physical Review E, 78 (4), 046110.Google Scholar
Leskovec, J., & Krevl, A. (2014) (June). SNAP Datasets: Stanford large network dataset collection. Retrieved from http://snap.stanford.edu/data.Google Scholar
Leskovec, J., Lang, K. J., Dasgupta, A., & Mahoney, M. W. (2008). Statistical properties of community structure in large social and information networks. In Proceedings of the 17th International Conference on World Wide Web. ACM, pp. 695–704.Google Scholar
Leskovec, J., Lang, K. J., & Mahoney, M. (2010). Empirical comparison of algorithms for network community detection. In Proceedings of the 19th International Conference on World Wide Web. ACM, pp. 631–640.CrossRefGoogle Scholar
Liben-Nowell, D., & Kleinberg, J. (2003). The link prediction problem for social networks. In Proceedings of the 12th International Conference on Information and Knowledge Management. ACM, pp. 556–559.Google Scholar
Long, B., Zhang, Z. M., & Yu, P. S. (2007). A probabilistic framework for relational clustering. In Proceedings of the 13th ACM sigkdd International Conference on Knowledge Discovery and Data Mining. ACM, pp. 470–479.Google Scholar
McDaid, A. F., Greene, D., & Hurley, N. (2011). Normalized mutual information to evaluate overlapping community finding algorithms. Oct. Retrieved from http://arxiv.org.Google Scholar
Mucha, P. J., Richardson, T., Macon, K., Porter, M. A., & Onnela, J.-P. (2010). Community structure in time-dependent, multiscale, and multiplex networks. Science, 328 (5980), 876–878.Google Scholar
Newman, M. (2009). Networks: an introduction. Oxford, England: OUP.Google Scholar
Newman, M. E. J. (2004). Fast algorithm for detecting community structure in networks. Physical Review E, 69 (6), 066133.Google Scholar
Newman, M. E. J., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69 (2), 026113.Google Scholar
Palla, G., Derényi, I., Farkas, I., & Vicsek, T. (2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature, 435 (7043), 814–818.Google Scholar
Porter, M. A., Onnela, J.-P., & Mucha, P. J. (2009). Communities in networks. Notices of the AMS, 56 (9), 1082–1097.Google Scholar
Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., & Parisi, D. (2004). Defining and identifying communities in networks. Proceedings of the National Academy of Sciences of the United States of America, 101 (9), 2658–2663.Google Scholar
Raghavan, U. N., Albert, R., & Kumara, S. (2007). Near linear time algorithm to detect community structures in large-scale networks. Physical Review E, 76 (3), 036106.Google Scholar
Reichardt, J., & Bornholdt, S. (2006a). Statistical mechanics of community detection. Physical Review E, 74 (1), 016110.Google Scholar
Reichardt, J., & Bornholdt, S. (2006b). Statistical mechanics of community detection. Physical Review E, 74 (1), 016110.Google Scholar
Rosvall, M., & Bergstrom, C. T. (2007). An information-theoretic framework for resolving community structure in complex networks. Proceedings of the National Academy of Sciences, 104 (18), 7327–7331.CrossRefGoogle ScholarPubMed
Rosvall, M., & Bergstrom, C. T. (2008). Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences, 105 (4), 1118–1123.CrossRefGoogle ScholarPubMed
Spielman, D. A., & Teng, S.-H. (2004). Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In Proceedings of the 36th Annual acm Symposium on Theory of Computing. ACM, pp. 81–90.Google Scholar
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of small-worldnetworks. Nature, 393 (6684), 440–442.Google Scholar
Wu, F., & Huberman, B. A. (2004). Finding communities in linear time: A physics approach. The European Physical Journal b-Bondensed Matter and Complex Systems, 38 (2), 331–338.Google Scholar
Xie, J., Kelley, S., & Szymanski, B. K. (2013). Overlapping community detection in networks: The state-of-the-art and comparative study. ACM Computing Surveys (csur), 45 (4), 43.Google Scholar
Xu, B., Liang, Z., Jia, Y., Zhou, B., & Han, Y. (2012). Local community detection using seeds expansion. In Proceedings of the 2nd International Conference on Cloud and Green Computing (cgc). IEEE, pp. 557–562.Google Scholar
Yang, J., & Leskovec, J. (2012). Defining and evaluating network communities based on ground-truth. In Proceedings of the ACM sigkdd Workshop on Mining Data Semantics. ACM, p. 3.Google Scholar
Yang, J., & Leskovec, J. (2013). Overlapping community detection at scale: A nonnegative matrix factorization approach. In Proceedings of the 6th ACM International Conference on Web Search and Data Mining. ACM, pp. 587–596.Google Scholar
Zachary, W. W. (1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33 (4), 452–473.Google Scholar