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ANNUAL REVIEWS

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Brain Graphs: Graphical Models of the Human Brain Connectome
Edward T. Bullmore1 and Danielle S. Bassett2
1 Behavioural & Clinical Neuroscience Institute, Department of Psychiatry,University of Cambridge, Cambridge Biomedical Campus, Cambridge CB2 0SZ, United Kingdom; email: etb23@cam.ac.uk 2 Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106

Annu. Rev. Clin. Psychol. 2011.7:113-140. Downloaded from www.annualreviews.org by Universidad de Chile on 04/19/11. For personal use only.

Annu. Rev. Clin. Psychol. 2011. 7:113–40 Firstpublished online as a Review in Advance on December 3, 2010 The Annual Review of Clinical Psychology is online at clinpsy.annualreviews.org This article’s doi: 10.1146/annurev-clinpsy-040510-143934 Copyright c 2011 by Annual Reviews. All rights reserved 548-5943/11/0427-0113$20.00

Keywords
network, systems, topological, connectome, connectivity, neuroimaging

Abstract
Brain graphs provide arelatively simple and increasingly popular way of modeling the human brain connectome, using graph theory to abstractly define a nervous system as a set of nodes (denoting anatomical regions or recording electrodes) and interconnecting edges (denoting structural or functional connections). Topological and geometrical properties of these graphs can be measured and compared to random graphs and tographs derived from other neuroscience data or other (nonneural) complex systems. Both structural and functional human brain graphs have consistently demonstrated key topological properties such as small-worldness, modularity, and heterogeneous degree distributions. Brain graphs are also physically embedded so as to nearly minimize wiring cost, a key geometric property. Here we offer a conceptualreview and methodological guide to graphical analysis of human neuroimaging data, with an emphasis on some of the key assumptions, issues, and trade-offs facing the investigator.

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Contents
WHAT IS A BRAIN GRAPH? . . . . . . . . WHY BOTHER WITH BRAIN GRAPHS AS MODELS OF THE HUMAN BRAIN CONNECTOME? . . . . . . . . . . . . . . . . Generalizability . . . . . . . . . . . . . . . . . . . .Interpretability . . . . . . . . . . . . . . . . . . . . Clinical Relevance . . . . . . . . . . . . . . . . . Caveats . . . . . . . . . . . . . . . . . . . . . . . . . . . . HOW TO CONSTRUCT A BRAIN GRAPH . . . . . . . . . . . . . . . . . . . What Is a Node? . . . . . . . . . . . . . . . . . . . What Is an Edge? . . . . . . . . . . . . . . . . . . MEASURES ON GRAPHS . . . . . . . . . . . TopologicalMeasures . . . . . . . . . . . . . . Geometric Measures . . . . . . . . . . . . . . . COMPARING AND VISUALIZING BRAIN GRAPHS . . . . . . . . . . . . . . . . . Comparing Graphs . . . . . . . . . . . . . . . . Visualizing Graphs . . . . . . . . . . . . . . . . . BEYOND THE SIMPLEST GRAPHS . . . . . . . . . . . . . . . . . . . . . . . . . Directional Connections and Causal Relationships . . . . . . . .Weighted Network Analysis . . . . . . . . CONCLUSIONS . . . . . . . . . . . . . . . . . . . . 114

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bedded, its geometrical properties can also be estimated and potentially related to network topology. To date, most such human brain graphs have specified binary connectivity—the edges between nodes are undirected andunweighted; see Figure 1. The construction of such binary brain graphs is the focus of this article, although we also briefly describe the construction of directed and/or weighted brain graphs.

Annu. Rev. Clin. Psychol. 2011.7:113-140. Downloaded from www.annualreviews.org by Universidad de Chile on 04/19/11. For personal use only.

WHY BOTHER WITH BRAIN GRAPHS AS MODELS OF THE HUMAN BRAIN...
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