Centrality and Peripherality in Filtered Graphs from Dynamical Financial Correlations

Minimum Spanning Trees and Planar Maximally Filtered Graphs are generated from correlations between $300$ most capitalized $NYSE$ stocks' daily returns, computed dynamically over moving windows of sizes between $1$ and $12$ months, in the period from $2001$ to $2003$. We study how different economic sectors differently populate the various regions of these graphs. We find that the financial sector is always at the center whereas the periphery is shared among different sectors. Four extremes are observed: stocks well connected and central; stocks well connected but at the same time peripheral; stocks poorly connected but central; stocks poorly connected and peripheral. Two principal components of centrality measures are individuated. The economic meaning of this hierarchical disposition is discussed. Suggested Reviewers: Response to Reviewers: We thank the reviewers for their careful scrutiny of the manuscript. All their suggestion where taken into account and the manuscript has been amended accordingly. We apologise for the inconveniencies caused by the bad LatTex format of the previous submission. July 14, 2008 3:57 WSPC/INSTRUCTION FILE ccpjune08 Advances in Complex Systems c © World Scientific Publishing Company Centrality and Peripherality in Filtered Graphs from dynamical Financial Correlations F. Pozzi, T. Di Matteo and T. Aste Department of Applied Mathematics, The Australian National University, 0200 Canberra, ACT, Australia. [email protected], [email protected], [email protected]. Received (22 /02 /2008) Revised (22 /05 /2008) Minimum Spanning Trees and Planar Maximally Filtered Graphs are generated from correlations between 300 most capitalized NY SE stocks’ daily returns, computed dynamically over moving windows of sizes between 1 and 12 months, in the period from 2001 to 2003. We study how different economic sectors differently populate the various regions of these graphs. We find that the financial sector is always at the center whereas the periphery is shared among different sectors. Four extremes are observed: stocks well connected and central; stocks well connected but at the same time peripheral; stocks poorly connected but central; stocks poorly connected and peripheral. Two principal components of centrality measures are individuated. The economic meaning of this hierarchical disposition is discussed.