On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
NP-complete decision problems for quadratic polynomials
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
On finding graph clusterings with maximum modularity
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Graph Spectra for Complex Networks
Graph Spectra for Complex Networks
Crawling and detecting community structure in online social networks using local information
IFIP'12 Proceedings of the 11th international IFIP TC 6 conference on Networking - Volume Part I
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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.