Exploring the Map Equation: Community Structure Detection in Unweighted, Undirected Networks
The map equation is one of the most efficient methods of evaluating a possible community structure of a network, computed by using Shanon’s entropy and probabilities that a random walker would exit a community or would wonder inside it. Infomap, the method that optimizes the map equation to reveal community structures, is one of the most efficient computational approach to this problem when dealing with weighted, directed or hierarchical networks. However, for some unweighted and undirected networks, Infomap fails completely to uncover any structure. In this paper we propose an alternate way of computing probabilities used by the map equation by adding information about 3-cliques corresponding to links in order to enhance the behavior of Infomap in unweighted networks. Numerical experiments performed on standard benchmarks show the potential of the approach.
KeywordsCommunity structure Social networks Unweighted graphs Infomap
This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS - UEFISCDI, project number PN-II-RU-TE-2014-4-2332.
- 2.Fortunato, S.: Community detection in graphs. Phys. Rep. 486, 75–174 (2010). http://www.sciencedirect.com/science/article/pii/S0370157309002841MathSciNetCrossRefGoogle Scholar
- 4.Gong, M., Ma, L., Zhang, Q., Jiao, L.: Community detection in networks by using multiobjective evolutionary algorithm with decomposition. Phys. A: Stat. Mech. Appl. 391(15), 4050–4060 (2012). http://www.sciencedirect.com/science/article/pii/S0378437112002579CrossRefGoogle Scholar
- 8.Lung, R., Suciu, M., Gasko, N.: Noisy extremal optimization. Soft Comput. 1–18 (2015). https://doi.org/10.1007/s00500-015-1858-3
- 11.Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948). https://doi.org/10.1002/j.1538-7305.1948.tb01338.xMathSciNetCrossRefMATHGoogle Scholar