Non-random topology of stock markets

Abstract

We have analysed the cross correlations of daily fluctuations for [iopmath latex="$N=6358$"] N = 6358 [/iopmath] US stock prices during the year 1999. From those [iopmath latex="$N(N-1)/2$"] N ( N -1)/2 [/iopmath] correlation coefficients, the minimum spanning tree (MST) has been built. We have investigated the topology exhibited by the MST. Even though the average coordination number of stocks is [iopmath latex="$langle n rangleapprox 2$"] n 2 [/iopmath], the variance [iopmath latex="$sigma$"] [/iopmath] of the topological distribution [iopmath latex="$f(n)$"] f ( n ) [/iopmath] diverges! More precisely, we have found that [iopmath latex="$f(n) sim n^{-2.2}$"] f ( n )~ n -super--2.2 [/iopmath] holds over two decades. We have studied the topological correlations for neighbouring nodes: an extremely broad set of local configurations exists, confirming the divergence of [iopmath latex="$sigma$"] [/iopmath].