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Small-World Brain Networks

Brain Mapping Unit, University of Cambridge, Department of Psychiatry, Addenbrooke’s Hospital, Cambridge, United Kingdom, Biological and Soft Systems, University of Cambridge, Department of Physics, Cavendish Laboratory, Cambridge, United Kingdom, Unit for Systems Neuroscience in Psychiatry, Genes, Cognition and Psychosis Program, National Institute of Mental Health, National Institutes of Health, Bethesda, Maryland

Ed Bullmore

Brain Mapping Unit, University of Cambridge, Department of Psychiatry, Addenbrooke’s Hospital, Cambridge, United Kingdom, etb23{at}cam.ac.uk

Many complex networks have a small-world topology characterized by dense local clustering or cliquishness of connections between neighboring nodes yet a short path length between any (distant) pair of nodes due to the existence of relatively few long-range connections. This is an attractive model for the organization of brain anatomical and functional networks because a small-world topology can support both segregated/specialized and distributed/integrated information processing. Moreover, small-world networks are economical, tending to minimize wiring costs while supporting high dynamical complexity. The authors introduce some of the key mathematical concepts in graph theory required for small-world analysis and review how these methods have been applied to quantification of cortical connectivity matrices derived from anatomical tract-tracing studies in the macaque monkey and the cat. The evolution of small-world networks is discussed in terms of a selection pressure to deliver cost-effective information-processing systems. The authors illustrate how these techniques and concepts are increasingly being applied to the analysis of human brain functional networks derived from electroencephalography/magnetoencephalography and fMRI experiments. Finally, the authors consider the relevance of small-world models for understanding the emergence of complex behaviors and the resilience of brain systems to pathological attack by disease or aberrant development. They conclude that small-world models provide a powerful and versatile approach to understanding the structure and function of human brain systems.

Key Words: Small-world network • Graph theory • Human brain functional networks • Functional magnetic resonance imaging

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