Although metaphorical and conceptual connections between the human brain and the financial markets have often been drawn, rigorous physical or mathematical underpinnings of this analogy remain largely unexplored. Here, we apply a statistical and graph theoretic approach to the study of two datasets – the time series of 90 stocks from the New York stock exchange over a 3-year period, and the fMRI-derived time series acquired from 90 brain regions over the course of a 10-min-long functional MRI scan of resting brain function in healthy volunteers. Despite the many obvious substantive differences between these two datasets, graphical analysis demonstrated striking commonalities in terms of global network topological properties. Both the human brain and the market networks were non-random, small-world, modular, hierarchical systems with fat-tailed degree distributions indicating the presence of highly connected hubs. These properties could not be trivially explained by the univariate time series statistics of stock price returns. This degree of topological isomorphism suggests that brains and markets can be regarded broadly as members of the same family of networks. The two systems, however, were not topologically identical. The financial market was more efficient and more modular – more highly optimized for information processing – than the brain networks; but also less robust to systemic disintegration as a result of hub deletion. We conclude that the conceptual connections between brains and markets are not merely metaphorical; rather these two information processing systems can be rigorously compared in the same mathematical language and turn out often to share important topological properties in common to some degree. There will be interesting scientific arbitrage opportunities in further work at the graph-theoretically mediated interface between systems neuroscience and the statistical physics of financial markets.
Keywords: human brain, networks, financial markets, fMRI, topology
Citation: Vértes PE, Nicol RM, Chapman SC, Watkins NW, Robertson DA and Bullmore ET (2011) Topological isomorphisms of human brain and financial market networks. Front. Syst. Neurosci. 5:75. doi: 10.3389/fnsys.2011.00075
Received: 30 May 2011; Paper pending published: 25 June 2011;
Accepted: 14 August 2011; Published online: 15 September 2011.
Edited by:Robert Turner, Max Planck Institute for Human Cognitive and Brain Sciences, Germany
Reviewed by:Marcus Kaiser, Seoul National University, South Korea
Copyright: © 2011 Vértes, Nicol, Chapman, Watkins, Robertson and Bullmore. This is an open-access article subject to a non-exclusive license between the authors and Frontiers Media SA, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and other Frontiers conditions are complied with.
*Correspondence: Edward T. Bullmore, Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Herchel Smith Building for Brain and Mind Sciences, Cambridge Biomedical Campus, Cambridge CB2 0SZ, UK. e-mail: firstname.lastname@example.org