Non-criticality of interaction network over system's crises: A percolation analysis

TL;DR

This paper investigates how financial market interaction networks behave around crises using percolation theory, revealing that they resemble critical random networks away from crises but deviate during crises.

Contribution

It introduces a percolation-based framework to analyze the aggregated behavior of financial interaction networks, highlighting their non-criticality during crises.

Findings

Interaction networks resemble Erdős-Rényi networks away from crises.

Networks deviate from critical behavior during crises.

Correlation growth alone does not explain the observed deviations.

Abstract

Extraction of interaction networks from multi-variate time-series is one of the topics of broad interest in complex systems. Although this method has a wide range of applications, most of the previous analyses have focused on the pairwise relations. Here we establish the potential of such a method to elicit aggregated behavior of the system by making a connection with the concepts from percolation theory. We study the dynamical interaction networks of a financial market extracted from the correlation network of indices, and build a weighted network. In correspondence with the percolation model, we find that away from financial crises the interaction network behaves like a critical random network of Erd\H{o}s-R\'{e}nyi, while close to a financial crisis, our model deviates from the critical random network and behaves differently at different size scales. We perform further analysis to clarify that our observation is not a simple consequence of the growth in correlations over the crises.