Centrality and Partial Correlation Coefficient-Based Assortativity Analysis of Real-World Networks

The assortativity index (A. Index) of a complex network has been hitherto computed as the Pearson's correlation coefficient of the remaining degree centrality (R-DEG) of the first-order neighbors (i.e. end vertices of the edges) in the network. In this paper, we seek to evaluate the assortativity of real-world networks with respect to prototypical centrality metrics (in addition to R-DEG) such as eigenvector centrality (EVC), betweenness centrality (BWC) and closeness centrality (CLC). Unlike R-DEG, the centrality values of the vertices with respect to these three metrics are influenced by the centrality values of the vertices in the neighborhood. We propose to use the notion of 'Partial Correlation Coefficient' to nullify the influence of the second-order neighbors (i.e. vertices that are two hops away) and quantify the assortativity of the first-order neighbors with respect to a particular centrality metric (such as EVC, BWC and CLC). We conduct an exhaustive assortativity analysis on a suite of 70 real-world networks of diverse degree distributions. We observe real-world networks to be more assortative (A. Index > 0) with respect to CLC and EVC and relatively more dissortative (A. Index < 0) with respect to BWC and R-DEG.