Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10: 186-198

University of Cambridge, Behavioural & Clinical Neurosciences Institute, Department of Psychiatry, Addenbrooke's Hospital, Cambridge, CB2 2QQ, UK.
Nature Reviews Neuroscience (Impact Factor: 31.43). 03/2009; 10(3):186-98. DOI: 10.1038/nrn2575
Source: PubMed


Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

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    • "Recent works have suggested that large-scale WM structural networks can be mapped from diffusion MRI tractography and analyzed with graph-theoretical approaches, that is, the so-called structural connectome (Bullmore and Sporns, 2009). Using connectome-based approaches, many studies have shown that human WM networks exhibit many nontrivial topological properties, such as smallworldness , modularity, and rich-club organization (Bullmore and Sporns, 2009; van den Heuvel and Sporns, 2011). "
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    ABSTRACT: Lifespan is a dynamic process with remarkable changes in brain structure and function. Previous neuroimaging studies have indicated age-related microstructural changes in specific white matter tracts during development and aging. However, the age-related alterations in the topological architecture of the white matter structural connectome across the human lifespan remain largely unknown. Here, a cohort of 113 healthy individuals (ages 9-85) with both diffusion and structural MRI acquisitions were examined. For each participant, the high-resolution white matter structural networks were constructed by deterministic fiber tractography among 1024 parcellation units and were quantified with graph theoretical analyses. The global network properties, including network strength, cost, topological efficiency, and robustness, followed an inverted U-shaped trajectory with a peak age around the third decade. The brain areas with the most significantly nonlinear changes were located in the prefrontal and temporal cortices. Different brain regions exhibited heterogeneous trajectories: the posterior cingulate and lateral temporal cortices displayed prolonged maturation/degeneration compared with the prefrontal cortices. Rich-club organization was evident across the lifespan, whereas hub integration decreased linearly with age, especially accompanied by the loss of frontal hubs and their connections. Additionally, age-related changes in structural connections were predominantly located within and between the prefrontal and temporal modules. Finally, based on the graph metrics of structural connectome, accurate predictions of individual age were obtained (r = 0.77). Together, the data indicated a dynamic topological organization of the brain structural connectome across human lifespan, which may provide possible structural substrates underlying functional and cognitive changes with age. Hum Brain Mapp, 2015. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.
    Full-text · Article · Jul 2015 · Human Brain Mapping
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    • "Finally , although the current GUI version of GRETNA includes several statistical functions , they are all parametric . Given the lack of statistical theory regarding the distribution of graph metrics for human brain networks , future versions could contain nonparametric inference of brain network metrics ( Bullmore and Sporns , 2009 ) , such as the permutation test ( Wang et al . , 2013 ) , Functional Data Analysis ( Bassett et al . "
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    ABSTRACT: Recent studies have suggested that the brain's structural and functional networks (i.e., connectomics) can be constructed by various imaging technologies (e.g., EEG/MEG; structural, diffusion and functional MRI) and further characterized by graph theory. Given the huge complexity of network construction, analysis and statistics, toolboxes incorporating these functions are largely lacking. Here, we developed the GRaph thEoreTical Network Analysis (GRETNA) toolbox for imaging connectomics. The GRETNA contains several key features as follows: (i) an open-source, Matlab-based, cross-platform (Windows and UNIX OS) package with a graphical user interface (GUI); (ii) allowing topological analyses of global and local network properties with parallel computing ability, independent of imaging modality and species; (iii) providing flexible manipulations in several key steps during network construction and analysis, which include network node definition, network connectivity processing, network type selection and choice of thresholding procedure; (iv) allowing statistical comparisons of global, nodal and connectional network metrics and assessments of relationship between these network metrics and clinical or behavioral variables of interest; and (v) including functionality in image preprocessing and network construction based on resting-state functional MRI (R-fMRI) data. After applying the GRETNA to a publicly released R-fMRI dataset of 54 healthy young adults, we demonstrated that human brain functional networks exhibit efficient small-world, assortative, hierarchical and modular organizations and possess highly connected hubs and that these findings are robust against different analytical strategies. With these efforts, we anticipate that GRETNA will accelerate imaging connectomics in an easy, quick and flexible manner. GRETNA is freely available on the NITRC website.
    Full-text · Article · Jun 2015 · Frontiers in Human Neuroscience
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    • "However , studies are beginning to adopt the view of the brain as a complex large-scale network characterized by interregional interactions . Along this line, graph theory offers a powerful approach for studying complex whole brain functional connectivity patterns (Bullmore and Sporns, 2009). As previously mentioned, studies have provided evidence that obesity is associated with functional differences in a widespread number of regions and components (e.g., Brooks et al., 2013; Kullmann et al., 2013). "
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    ABSTRACT: Obesity is associated with structural and functional alterations in brain areas that are often functionally distinct and anatomically distant. This suggests that obesity is associated with differences in functional connectivity of regions distributed across the brain. However, studies addressing whole brain functional connectivity in obesity remain scarce. Here, we compared voxel-wise degree centrality and eigenvector centrality between participants with obesity (n=20) and normal-weight controls (n=21). We analyzed resting state and task-related fMRI data acquired from the same individuals. Relative to normal-weight controls, participants with obesity exhibited reduced degree centrality in the right middle frontal gyrus in the resting-state condition. During the task fMRI condition, obese participants exhibited less degree centrality in the left middle frontal gyrus and the lateral occipital cortex along with reduced eigenvector centrality in the lateral occipital cortex and occipital pole. Our results highlight the central role of the middle frontal gyrus in the pathophysiology of obesity, a structure involved in several brain circuits signaling attention, executive functions and motor functions. Additionally, our analysis suggests the existence of task-dependent reduced centrality in occipital areas; regions with a role in perceptual processes and that are profoundly modulated by attention. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.
    Full-text · Article · Jun 2015 · Psychiatry Research: Neuroimaging
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