Higher-Order Aggregate Networks in the Analysis of Temporal Networks: Path structures and centralities

TL;DR

This paper demonstrates that higher-order aggregate networks provide more accurate measures of node importance in temporal networks than traditional static representations, revealing the impact of link order on centrality.

Contribution

It introduces a second-order aggregate network approach for better capturing temporal path-based centralities, improving analysis accuracy over static models.

Findings

Higher-order networks outperform static models in capturing true node centralities.

Static, time-aggregated analysis can misrepresent node importance.

Second-order centrality measures align more closely with actual temporal importance.

Abstract

Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in which links occur in real-world temporal networks affects causality structures and thus the evolution of dynamical processes, and ii) higher-order aggregate representations of temporal networks can be used to analytically study the effect of these order correlations on dynamical processes. In this article we analyze the effect of order correlations on path-based centrality measures in real-world temporal networks. Analyzing temporal equivalents of betweenness, closeness and reach centrality in six empirical temporal networks, we first show that an analysis of the commonly used static, time-aggregated representation can give misleading results about the actual importance of nodes. We further study higher-order time-aggregated networks, a recently proposed generalization of the commonly applied static, time-aggregated representation of temporal networks. Here, we particularly define path-based centrality measures based on second-order aggregate networks, empirically validating that node centralities calculated in this way better capture the true temporal centralities of nodes than node centralities calculated based on the commonly used static (first-order) representation. Apart from providing a simple and practical method for the approximation of path-based centralities in temporal networks, our results highlight interesting perspectives for the use of higher-order aggregate networks in the analysis of time-stamped network data.