A Modular Framework for Centrality and Clustering in Complex Networks

Abstract

The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important such network analysis techniques, namely, centrality and clustering. An information-flow based model is adopted for clustering, which itself builds upon an information theoretic measure for computing centrality. Our principal contributions include (1) a generalized model of Markov entropic centrality with the flexibility to tune the importance of node degrees, edge weights and directions, with a closed-form asymptotic analysis, which (2) leads to a novel two-stage graph clustering algorithm. The centrality analysis helps reason about the suitability of our approach to cluster a given graph, and determine ‘query’ nodes, around which to explore local community structures, leading to an agglomerative clustering mechanism. Our clustering algorithm naturally inherits the flexibility to accommodate edge directionality, as well as different interpretations and interplay between edge weights and node degrees. Extensive benchmarking experiments are provided, using both real-world networks with ground truth and synthetic networks.