# Evaluating structural edge importance in temporal networks

Authors
• 1 Financial Conduct Authority, Endeavour Square, London, United Kingdom , London (United Kingdom)
• 2 University College London, London, United Kingdom , London (United Kingdom)
• 3 London School of Economics, London, United Kingdom , London (United Kingdom)
• 4 London Mathematical Laboratory, London, United Kingdom , London (United Kingdom)
Type
Published Article
Journal
EPJ Data Science
Publisher
Springer Berlin Heidelberg
Publication Date
May 08, 2021
Volume
10
Issue
1
Identifiers
DOI: 10.1140/epjds/s13688-021-00279-6
Source
Springer Nature
Keywords
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 le\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$l_{e}$\end{document}—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 le\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$l_{e}$\end{document}. We then estimate the model parameters associated with five real financial and social networks, and we study their predictability. These methods have applications 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.