  Modularity, first proposed by [Newman and Girvan, 2004], is one of the most
popular ways to quantify the significance of community structure in complex
networks. It can serve as both a standard benchmark to compare different
community detection algorithms, and an optimization objective to detect
communities itself. Previous work on modularity has developed many efficient
algorithms for modularity maximization. However, few of researchers considered
the interpretation of the modularity function itself. In this paper, we study
modularity from an information-theoretical perspective and show that modularity
and mutual information in networks are essentially the same. The main
contribution is that we develop a family of generalized modularity measures,
f-modularity based on f-mutual information. f-Modularity has an
information-theoretical interpretation, enjoys the desired properties of mutual
information measure, and provides an approach to estimate the mutual
information between discrete random variables. At a high level, we show the
significance of community structure is equivalent to the amount of information
contained in the network. The connection of f-modularity and f-mutual
information bridges two important fields, complex network and information
theory and also sheds light on the design of measures on community structure in
future.
