"Cross-Linked Structure of Network Evolution"

A new paper of mine was published in final form today. In this paper, my coauthors and I use a structure called a "cross-link" that connects a pair of time-dependent edges based on the similarity of their temporal evolution. In our study, the time-dependent edges arise from similarity of temporal dynamics of different nodes. The basic idea is to try to tease out when sets of edges evolve separately and when there is co-evolution. In this paper, we consider time-dependent networks that we construct from time series from functional brain networks and from output of coupled Kuramoto oscillators. Here are the details of the paper.


Title: Cross-Linked Structure of Network Evolution

Authors: Danielle S. Bassett, Nicholas F. Wymbs, Mason A. Porter, Peter J. Mucha, and Scott T. Grafton

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. 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.