Evaluating structural edge importance in temporal networks

TL;DR

This paper introduces a spectral importance metric for edges in temporal networks, demonstrating its use in predicting network evolution and its applications in financial regulation and understanding micro-macro network dynamics.

Contribution

The paper proposes a novel spectral importance metric for edges and a model linking this metric to network evolution, validated on synthetic and real data.

Findings

The spectral importance metric correlates with edge change likelihood.

The model predicts edge changes with measurable accuracy.

Applications include financial regulation and network analysis insights.

Abstract

To monitor risk in temporal financial networks, we need to understand how individual behaviours affect the global evolution of networks. Here we define a structural importance metric - which we denote as $l_e$ - for the edges of a network. The metric is based on perturbing the adjacency matrix and observing the resultant change in its largest eigenvalues. We then propose a model of network evolution where this metric controls the probabilities of subsequent edge changes. We show using synthetic data how the parameters of the model are related to the capability of predicting whether an edge will change from its value of $l_e$. We then estimate the model parameters associated with five real financial and social networks, and we study their predictability. These methods have application in financial regulation whereby it is important to understand how individual changes to financial networks will impact their global behaviour. It also provides fundamental insights into spectral predictability in networks, and it demonstrates how spectral perturbations can be a useful tool in understanding the interplay between micro and macro features of networks.