Local clustering coefficient-based assortativity analysis of real-world network graphs

Abstract

Assortative index (A. Index) of a network graph is a measure of the similarity of the end vertices of the edges with respect to a node-level metric. Networks were classified as assortative, dissortative or neutral depending on the proximity of the A. index values to 1, -1 or 0 respectively. Degree centrality (DegC) has been traditionally the node-level metric used for assortativity analysis in the literature. In this paper, we propose to analyse assortativity of real-world networks using the local clustering coefficient (LCC) metric: a measure of the probability with which any two neighbours of a vertex are connected. Though DegC and LCC are inversely related, we observe 80% of the 50 real-world network graphs analysed to exhibit similar levels of assortativity. We also observe a real-world network graph to be neutral (i.e., assortative or dissortative) with a probability of 0.6 or above with respect to both DegC and LCC.