Entropy of Graphs in Financial Markets

Abstract

This article analyzes the eigenvalues of financial graphs and discusses different types of graphs using random graph theory. We found that the energy-based Renyi index is an effective tool for studying the spectrum of financial graphs. The entropy of financial graphs is usually different from the theoretical predictions of random graph theory, which implies the existence of rich structures. This article also constructed some benchmark graphs for comparative analysis through the classic financial models. The calculations show that the geometric Brownian motion and the one factor model correspond to completely different entropy values based on eigenvalues, thus providing two extreme cases for characterizing real graph entropy. In particular, we find a high correlation between the degree-based Renyi index and the eigenvalue-based Renyi index based on real market data. This article shows the analysis of the structure and complexity of financial graphs from the perspective of graph entropy, thus providing a new way to analyze different types of financial graphs.