An Empirical Study of the Relation between Community Structure and Transitivity
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.
KeywordsCommunity Structure Degree Distribution Community Detection Transitive Network Community Detection Algorithm
Unable to display preview. Download preview PDF.
- 1.Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E 69 (2004)Google Scholar
- 6.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)Google Scholar
- 11.Newman, M.E.J.: Random Graphs with Clustering. Phys. Rev. Lett. 103 (2009)Google Scholar
- 19.Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. P10008 (2008)Google Scholar
- 22.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 0711.3199Google Scholar
- 23.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)Google Scholar