Δ-Conformity: Multi-scale Node Assortativity in Feature-rich Stream Graphs

Abstract

Heterogeneity is a key aspect of complex networks, often emerging by looking at the distribution of node properties, from the milestone observations on the degree to the recent developments in mixing pattern estimation. Mixing patterns, in particular, refer to nodes' connectivity preferences with respect to an attribute label. Social networks are mostly characterized by assortative/homophilic behaviour, where nodes are more likely to be connected with similar ones. Recently, assortative mixing is increasingly measured in a multi-scale fashion to overcome well-known limitations of classic scores. Such multi-scale strategies can capture heterogeneous behaviors among node homophily, but they ignore an important, often available, addendum in real-world systems: the time when edges are present and the time-varying paths they form accordingly. Hence, temporal homophily is still little understood in complex networks. In this work we aim to cover this gap by introducing the ∆-Conformity measure, a multi-scale, path-aware, node homophily estimator within the new framework of feature-rich stream graphs. A rich experimental section analyzes ∆-Conformity trends over time, spanning the analysis from real-life social interaction networks to a specific case-study about the Bitcoin Transaction Network.