Cross-Linked Structure of Network Evolution

TL;DR

This paper explores the cross-link structures in temporal networks using hypergraphs, revealing co-evolution patterns in systems like coupled oscillators and brain activity during learning, demonstrating the method's effectiveness.

Contribution

It introduces a hypergraph-based approach to analyze cross-link structures in temporal networks, uncovering co-evolution patterns and emergent subgraphs in real and synthetic data.

Findings

Hyperedges reveal co-evolution patterns within and between communities.

Brain networks show early co-evolution that stabilizes with practice.

Cross-link analysis uncovers unexpected co-evolution attributes.

Abstract

We study the temporal co-variation of network co-evolution via the cross-link structure of networks, for which we take advantage of the formalism of hypergraphs to map cross-link structures back to network nodes. We investigate two sets of temporal network data in detail. In a network of coupled nonlinear oscillators, hyperedges that consist of network edges with temporally co-varying weights uncover the driving co-evolution patterns of edge weight dynamics both within and between oscillator communities. In the human brain, networks that represent temporal changes in brain activity during learning exhibit early co-evolution that then settles down with practice, and subsequent decreases in hyperedge size are consistent with emergence of an autonomous subgraph whose dynamics no longer depends on other parts of the network. Our results on real and synthetic networks give a poignant demonstration of the ability of cross-link structure to uncover unexpected co-evolution attributes in both real and synthetic dynamical systems. This, in turn, illustrates the utility of analyzing cross-links for investigating the structure of temporal networks.