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Non-random topology of stock markets 

Authors: N. Vandewalle a;  F. Brisbois a; X. Tordoir b
Affiliations:   a GRASP, Institut de Physique B5, Universiteacute de Liegravege, B-4000 Liegravege, Belgium.
b IPNE, B15, Universiteacute de Liegravege, B-4000 Liegravege, Belgium.
DOI: 10.1088/1469-7688/1/3/308
Publication Frequency: 8 issues per year
Published in: journal Quantitative Finance, Volume 1, Issue 3 March 2001 , pages 372 - 374
Formats available: PDF (English)
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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="$langle n rangleapprox 2$"] n2 [/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="$f(n) sim n^lcub-2.2rcub$"] f(n)~n-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] .
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