Self-organized critical topology of stock markets

TL;DR

This paper analyzes the topology of stock market correlations using Minimum Spanning Trees, revealing a self-organized critical structure with a power-law degree distribution and broad local configurations.

Contribution

It introduces a novel application of MST topology analysis to stock markets, uncovering a self-organized critical state with a power-law degree distribution.

Findings

Degree distribution follows a power-law with exponent -2.2

Average node degree is about 2, but variance diverges

Local topological configurations are extremely broad

Abstract

We have analyzed the cross-correlations of daily fluctuations for N=6 358 US stock prices during the year 1999. From those $N(N-1)/2$ correlations coefficients, the Minimum Spanning Tree (MST) has been built. We have investigated the topology exhibited by the MST. Eventhough the average topological number is $<n > \approx 2$, the variance $\sigma$ of the topological distribution f(n) diverges. More precisely, we have found that $f(n) \sim n^{-2.2}$ holding over two decades. We have studied the topological correlations for neighbouring nodes: an extremely broad set of local configurations exists, confirming the divergence of $\sigma$.