Temporal-topological properties of higher-order evolving networks

TL;DR

This paper introduces methods to analyze the temporal and topological properties of higher-order interactions in evolving networks, revealing distinct patterns in physical contact versus collaboration networks and aiding future dynamic process modeling.

Contribution

The paper develops novel techniques to characterize higher-order temporal-topological properties in evolving networks, enabling comparison and understanding of their dynamic behaviors.

Findings

Physical contact networks show temporal and topological correlations in higher-order events.

Nodes involved in multiple groups tend to participate across different event orders.

Collaboration networks lack the observed temporal-topological correlations present in physical contact networks.

Abstract

Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more than two people. Such group interactions can be represented as higher-order events of an evolving network. Here, we propose methods to characterize the temporal-topological properties of higher-order events to compare networks and identify their (dis)similarities. We analyzed 8 real-world physical contact networks, finding the following: a) Events of different orders close in time tend to be also close in topology; b) Nodes participating in many different groups (events) of a given order tend to involve in many different groups (events) of another order; Thus, individuals tend to be consistently active or inactive in events across orders; c) Local events that are close in topology are correlated in time, supporting observation a). Differently, in 5 collaboration networks, observation a) is almost absent; Consistently, no evident temporal correlation of local events has been observed in collaboration networks. Such differences between the two classes of networks may be explained by the fact that physical contacts are proximity based, in contrast to collaboration networks. Our methods may facilitate the investigation of how properties of higher-order events affect dynamic processes unfolding on them and possibly inspire the development of more refined models of higher-order time-varying networks.