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Here we consider generative models for the probability of a functional connection (an edge) between two cortical regions (nodes) separated by some Euclidean distance in anatomical space. In particular, we propose a model in which the embedded topology of brain networks emerges from two competing factors: a distance penalty based on the cost of maintaining long-range connections; and a topological term that favors links between regions sharing similar input. We show that, together, these two biologically plausible factors are sufficient to capture an impressive range of topological properties of functional brain networks. Model parameters estimated in one set of functional MRI (fMRI) data on normal volunteers provided a good fit to networks estimated in a second independent sample of fMRI data. Furthermore, slightly detuned model parameters also generated a reasonable simulation of the abnormal properties of brain functional networks in people with schizophrenia. We therefore anticipate that many aspects of brain network organization, in health and disease, may be parsimoniously explained by an economical clustering rule for the probability of functional connectivity between different brain areas.<\/jats:p>","DOI":"10.1073\/pnas.1111738109","type":"journal-article","created":{"date-parts":[[2012,3,31]],"date-time":"2012-03-31T00:38:19Z","timestamp":1333154299000},"page":"5868-5873","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":332,"title":["Simple models of human brain functional networks"],"prefix":"10.1073","volume":"109","author":[{"given":"Petra E.","family":"V\u00e9rtes","sequence":"first","affiliation":[{"name":"Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ, United Kingdom;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aaron F.","family":"Alexander-Bloch","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ, United Kingdom;"},{"name":"Child Psychiatry Branch, National Institute of Mental Health, Bethesda, MD 20892-1600;"},{"name":"David Geffen School of Medicine at University of California, Los Angeles, CA 90095;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nitin","family":"Gogtay","sequence":"additional","affiliation":[{"name":"Child Psychiatry Branch, National Institute of Mental Health, Bethesda, MD 20892-1600;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jay N.","family":"Giedd","sequence":"additional","affiliation":[{"name":"Child Psychiatry Branch, National Institute of Mental Health, Bethesda, MD 20892-1600;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Judith L.","family":"Rapoport","sequence":"additional","affiliation":[{"name":"Child Psychiatry Branch, National Institute of Mental Health, Bethesda, MD 20892-1600;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edward T.","family":"Bullmore","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ, United Kingdom;"},{"name":"Cambridgeshire and Peterborough National Health Service Foundation Trust, Cambridge CB21 5EF, United Kingdom; and"},{"name":"GlaxoSmithKline Clinical Unit Cambridge, Addenbrookes Hospital, Cambridge CB2 0QQ, United Kingdom"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2012,3,30]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1186\/1753-4631-1-3","article-title":"Graph theoretical analysis of complex networks in the brain","volume":"1","author":"Stam CJ","year":"2007","unstructured":"CJ Stam, JC Reijneveld, Graph theoretical analysis of complex networks in the brain. 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