Abstract
One of the most prominent properties in real-world networks is the presence of a community structure, i.e. dense and loosely interconnected groups of nodes called communities. In an attempt to better understand this concept, we study the relationship between the strength of the community structure and the network transitivity (or clustering coefficient). Although intuitively appealing, this analysis was not performed before. We adopt an approach based on random models to empirically study how one property varies depending on the other. It turns out the transitivity increases with the community structure strength, and is also affected by the distribution of the community sizes. Furthermore, increasing the transitivity also results in a stronger community structure. More surprisingly, if a very weak community structure causes almost zero transitivity, the opposite is not true and a network with a close to zero transitivity can still have a clearly defined community structure. Further analytical work is necessary to characterize the exact nature of the identified relationship.
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References
Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E 69 (2004)
Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)
Pastor-Satorras, R., Rubi, M., Diaz-Guilera, A., Barabási, A.-L., Ravasz, E., Oltvai, Z.: Hierarchical Organization of Modularity in Complex Networks. In: Statistical Mechanics of Complex Networks, vol. 625, pp. 46–65. Springer, Heidelberg (2003)
Clauset, A., Moore, C., Newman, M.E.J.: Hierarchical structure and the prediction of missing links in networks. Nature 453, 98–101 (2008)
Liu, Z.H.: Bambi: Epidemic spreading in community networks. Europhysics Letters 72, 315–321 (2005)
Wang, G.-X., Qin, T.-G.: Impact of Community Structure on Network Efficiency and Communicability. In: 2010 International Conference on Intelligent Computation Technology and Automation (ICICTA), vol. 2, pp. 485–488 (2010)
Watts, D., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 409–410 (1998)
Jin, E.M., Girvan, M., Newman, M.E.J.: Structure of growing social networks. Phys. Rev. E 64, 046132 (2001)
Boguña, M., Pastor-Satorras, R., Diaz-Guilera, A., Arenas, A.: Models of social networks based on social distance attachment. Phys. Rev. E 70, 056122 (2004)
Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys Rev E 78, 046110 (2008)
Newman, M.E.J.: Random Graphs with Clustering. Phys. Rev. Lett. 103 (2009)
Fortunato, S.: Community detection in graphs. Physics Reports 486, 75–174 (2010)
Fortunato, S., Barthelemy, M.: Resolution limit in community detection. PNAS USA 104, 36–41 (2007)
Luce, R.D., Perry, A.D.: A method of matrix analysis of group structure. Psychometrika 14, 95–116 (1949)
Lancichinetti, A., Kivelä, M., Saramäki, J., Fortunato, S.: Characterizing the Community Structure of Complex Networks. PLoS ONE 5, e11976 (2010)
Molloy, M., Reed, B.: A critical point for random graphs with a given degree sequence. Random Structures and Algorithms 6, 161–179 (1995)
Barabasi, A., Albert, R.: Emergence of scaling in random networks. Science 286, 509 (1999)
Poncela, J., Gomez-Gardeñes, J., Florıa, L.M., Sanchez, A., Moreno, Y.: Complex Cooperative Networks from Evolutionary Preferential Attachment. PLoS ONE 3, e2449 (2008)
Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. P10008 (2008)
Rosvall, M., Bergstrom, C.T.: Maps of random walks on complex networks reveal community structure. PNAS 105, 1118 (2008)
Orman, G.K., Labatut, V., Cherifi, H.: Qualitative Comparison of Community Detection Algorithms. Communications in Computer and Information Science 167, 265–279 (2011)
da Fontoura Costa, L., Oliveira Jr., O.N., Travieso, G., Rodrigues, R.A., Villas Boas, P.R., Antiqueira, L., Viana, M.P., da Rocha, L.E.C.: Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications (2008), arXiv 0711.3199
Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Statistical Properties of Community Structure in Large Social and Information Networks. In: WWW. ACM, Beijing (2008)
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Orman, K., Labatut, V., Cherifi, H. (2013). An Empirical Study of the Relation between Community Structure and Transitivity. In: Menezes, R., Evsukoff, A., González, M. (eds) Complex Networks. Studies in Computational Intelligence, vol 424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30287-9_11
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DOI: https://doi.org/10.1007/978-3-642-30287-9_11
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