Evaluating structural edge importance in temporal networks
Financial Conduct Authority, Endeavour Square, London, United Kingdom
2 Department of Computer Science, University College London, London, United Kingdom
3 Systemic Risk Centre, London School of Economics, London, United Kingdom
4 London Mathematical Laboratory, London, United Kingdom
Accepted: 3 May 2021
Published online: 8 May 2021
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 —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 . 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.
Key words: Spectral perturbation / Dynamics / Edge predictability / Classification
© The Author(s) 2021
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