$$\Delta $$-Conformity: multi-scale node assortativity in feature-rich stream graphs

Abstract

AbstractMulti-scale strategies to estimate mixing patterns are meant to capture heterogeneous behaviors among node homophily, but they ignore an important addendum often available in real-world networks: the time when edges are present and the time-varying paths that edges form accordingly. In this work, we go beyond the assumption of a static network topology to propose a multi-scale, path- and time-aware node homophily estimator specifically tied for feature-rich stream graphs: $$\Delta $$ Δ -Conformity. Our measure can capture the homogeneous/heterogeneous tendency of nodes’ connectivity along a period of time $$\Delta $$ Δ starting from a given moment in time. Results on face-to-face interaction networks suggest it is possible to track changes in social mixing behaviors that coincide with contextually reasonable everyday patterns, e.g., medical staff disassortative behavior when exposed to patients. In a different domain, that of the Bitcoin Transaction Network, we capture relationships between the quantity of money sent from (and to) different categories/continents and their respective mixing trends over time. All these insights help us to introduce $$\Delta $$ Δ -Conformity as a suitable solution for understanding temporal homophily by capturing the mixing tendency of entities embedded in fine-grained evolving contexts.