Sparsity of weighted networks: measures and applications

TL;DR

This paper introduces a sparsity index for weighted networks that characterizes their structural diversity, analyzes its properties, and demonstrates its application in community detection with validated results on real and artificial networks.

Contribution

It develops a novel sparsity measure for weighted networks, derives its properties analytically, and applies it effectively to community detection tasks.

Findings

Sparsity index ranges are analytically derived for connected networks.

Edge-weight distribution impacts the sparsity index bounds.

Application in community detection shows improved network analysis.

Abstract

A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index defined on ordered degree sequence of simple networks and derives further properties of this index. 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; a pattern is uncovered in corresponding degree sequences to produce highest sparsities. Given the edge-weight frequency distribution of a network, we have formulated an expression of the sparsity index of edge-weights. 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, having 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 has been demonstrated through overlapping community detection of networks. The results validated on artificial and real-world networks show its efficacy.