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Comparing brain networks of different size and connectivity density using graph theory

van Wijk, BC; Stam, CJ; Daffertshofer, A; (2010) Comparing brain networks of different size and connectivity density using graph theory. PLoS One , 5 (10) , Article e13701. 10.1371/journal.pone.0013701. Green open access

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Abstract

Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others.

Type: Article
Title: Comparing brain networks of different size and connectivity density using graph theory
Location: United States
Open access status: An open access version is available from UCL Discovery
DOI: 10.1371/journal.pone.0013701
Publisher version: http://dx.doi.org/10.1371/journal.pone.0013701
Language: English
Additional information: © 2010 van Wijk et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. PMCID: PMC2965659
Keywords: Brain, Humans
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology > Department of Neuromuscular Diseases
URI: https://discovery.ucl.ac.uk/id/eprint/1401865
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