Generating Hierarchically Modular Networks via Link Switching

Abstract: This paper introduces a method to generate hierarchically modular networks with prescribed node degree list by link switching. Unlike many existing network generating models, our method does not use link probabilities to achieve modularity. Instead, it utilizes a user-specified topology to determine relatedness between pairs of nodes in terms of edge distances and links are switched to increase edge distances. To measure the modular-ness of a network as a whole, a new metric called Q2 is proposed. Comparisons are made between the Q [15] and Q2 measures. We also comment on the effect of our modularization method on other network characteristics such as clustering, hierarchy, average path length, small-worldness, degree correlation and centrality. An application of this method is reported elsewhere [12]. Briefly, the generated networks are used as test problems to explore the effect of modularity and degree distribution on evolutionary search algorithms.