![]() ( A) Nodal strength is the sum of the associations between the index node and all other nodes in the system, and edge diversity is defined as the standard deviation of the associations. 2006).įigure 3 Schematic definitions of basic connectivity and graph metrics. The correlation or partial correlation of these regional morphometric variables over subjects provides an association matrix ( right), which can be used as a measure of anatomical connectivity ( Lerch et al. ( C) Several morphometric variables can be computed on a regional basis ( left) from individual structural MRI images, including gray matter volume, cortical thickness, surface area, and curvature ( middle). Due to this increase in temporal resolution, a wide variety of association metrics can be applied, including mutual information, synchronization, and phase coherence ( right), to construct an association matrix. ( B) For EEG or MEG data, neurophysiological time series are measured by an array of sensors ( left), each of which provides a nodal time series ( middle) at frequencies generally higher than those measured by fMRI. If we choose the measure of association to be the absolute Pearson's correlation between two time series, then this value ranges between 0 and 1. The pair-wise association a i, j is estimated between the ith and jth nodes, i≠ j=1, 2, 3, …, N and compiled for all possible pairs to form a interregional association matrix, A ( right). Regional mean time series ( middle) are estimated for each of the N = 90 regions in the parcellation template. ( A) An anatomical template image ( left) is used to parcellate the voxel-level fMRI data. Edges connecting nodes are unweighted or binary (they are either present or not present) and undirected (if an edge links node i to node j, it also links node j to node i).įigure 2 From data to association matrix. Circles indicate regional nodes of the brain network gray lines indicate connections between them. This heterogeneity is the necessary substrate for nodes to perform a broad range of functional roles. The human brain network, as measured by both structural and functional neuroimaging, lies in between these two extremes and displays a broad-scale degree distribution where low-degree nodes, medium-degree nodes, and high-degree nodes coexist in unison and collectively form the network architecture. In contrast, a star network ( upper left) is maximally heterogeneous, with a single high-degree hub and many low-degree peripheral nodes. Random and regular networks, although differing in terms of order/disorder, both have homogeneous degree distributions that is, all nodes are connected to roughly the same number of other nodes. Small-world networks, like the brain, exist between the extreme boundaries of a regular lattice network ( lower left) and pure random network ( lower right). Keywordsįigure 1 Organization of human brain networks in comparison to extremal architectures on topological dimensions of small-worldness ( x-axis) and degree distribution ( y-axis). Here we offer a conceptual review 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. Brain graphs are also physically embedded so as to nearly minimize wiring cost, a key geometric property. Both structural and functional human brain graphs have consistently demonstrated key topological properties such as small-worldness, modularity, and heterogeneous degree distributions. Topological and geometrical properties of these graphs can be measured and compared to random graphs and to graphs derived from other neuroscience data or other (nonneural) complex systems. Brain graphs provide a relatively 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).
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