Structural and functional analytics for community detection in large-scale complex networks

Abstract

Community structure is thought to be one of the main organizing principles in most complex networks. Big data and complex networks represent an area which researchers are analyzing worldwide. Of special interest are groups of vertices within which connections are dense. In this paper we begin with discussing community dynamics and exploring complex network structural parameters. We put forward structural and functional models for analyzing complex networks under situations of perturbations. We introduce modified adjacency and modified Laplacian matrices. We further introduce network or degree centrality (weighted Laplacian centrality) based on modified Laplacian, weighted micro-community centrality. We discuss its robustness and importance for micro-community detection for social and technological complex networks with overlapping communities. We also introduce ’k-clique sub-community’ overlapping community detection based on degree and weighted micro-community centrality. The proposed algorithms use optimal partition of k-clique sub-community for modularity optimization. We establish relationship between degree centrality and modularity. This proposed method with modified adjacency matrix helps us solve NP-hard problem.