Generating graphs that approach a prescribed modularity

• Published in: Computer communications Vol. 36; no. 4; pp. 363 - 372
• Main Authors: Trajanovski, S., Kuipers, F.A., Martín-Hernández, J., Van Mieghem, P.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 15-02-2013; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Exact sciences and technology; Graph generator; Information retrieval. Graph; Modeling community structure; Modularity; Software; Theoretical computing; Graph generator; Modeling community structure; Modularity; Network structure; Modular system; Heuristic method; Cluster; NP complete problem; Social network; Topology; Modeling
• ISSN: 0140-3664; 1873-703X
• DOI: 10.1016/j.comcom.2012.10.004

Modularity is a quantitative measure for characterizing the existence of a community structure in a network. A network’s modularity depends on the chosen partitioning of the network into communities, which makes finding the specific partition that leads to the maximum modularity a hard problem. In this paper, we prove that deciding whether a graph with a given number of links, number of communities, and modularity exists is NP-complete and subsequently propose a heuristic algorithm for generating graphs with a given modularity. Our graph generator allows constructing graphs with a given number of links and different topological properties. The generator can be used in the broad field of modeling and analyzing clustered social or organizational networks.