Sparsity of weighted networks: Measures and applications

Abstract

A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as an indicator of inherent diversity of different network parameters. The measure called sparsity index defined on ordered degree sequence of simple networks is extended and new properties of this index are derived. The range of possible values of sparsity index of any connected network, with edge-count in specific intervals, is worked out analytically in terms of node-count and a pattern is uncovered in corresponding degree sequences. Given the edge-weight frequency distribution of a network, an expression of the sparsity index of edge-weights is formulated. Its properties are analyzed under different distributions of edge-weights. For example, the upper and lower bounds of sparsity index of edge-weights of a network, with all distinct edge-weights, is determined in terms of its node-count and edge-density. The article highlights that this summary index with low computational cost, computed on different network parameters, is useful to reveal different structural and organizational aspects of networks for performing analysis. An application of this index is demonstrated through devising a new overlapping community detection method. The results validated on artificial and real-world networks show its efficacy.