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2, restricted to the nodes in N1. HN1 provides the measure of the this website distance from zero correlation. The amount of correlation between two regions N1 and N2 is computed through their mutual information, namely (6) To adapt graphical representations for this analysis and to allow a comparison between AD patients and controls, we ranked the intra- and inter-lobar associations into three levels (weak, medium, and strong) via a K-means algorithm. In the conventional topological approach, we studied various metrics introduced in the complex network field including node centrality, global efficiency, local efficiency, and modularity (Boccaletti et al. 2006; Bullmore and Sporns 2009). Let us denote by A = aij the adjacency matrix of a binary undirected network G, where an element aij is nonnull, if an edge between nodes i and j exists. The degree of a node i is defined as (7) where V is the set of all nodes of G. The degree of a node is considered a measure of node centrality. Nodes with a centrality value lying in the upper quartile of the integrated (see below for details) node degree distribution were defined as hubs (Sporns et al. 2007). Global efficiency is equivalent to the inverse of the harmonic mean of the length of the shortest paths in each pair of nodes in the network, whereas local efficiency is restricted to the topological first neighbors. In other words, global efficiency is related to global interconnectedness, whereas local efficiency is related Selleck Sotrastaurin to local interconnectedness (Latora and Marchiori 2001). In formulae, efficiency is defined as (8) where NV is the number of the nodes of network G, and dij is the length of FMO4 the shortest path between nodes i and j. The definitions of global and local efficiency follow as (9) where Gi is the sub-network composed of the first-order (topological) neighborhood of node i. A module is defined as a group of nodes connected by a larger number of within-group edges than between-group edges (i.e., connecting the group with the rest of the node groups). The Q index quantifies the degree of modularity of G and is calculated as in (Newman 2006). (10) where m is the predetermined set of modules with nonoverlapping nodes, and eij stands for the proportion of all links connecting nodes in module i with those in module j. Q quantifies the degree of a modular structure with m modules, in which the larger the Q, the more modular the network. We investigated these four metrics over a range of densities chosen according to the lfdr statistics such that 0.2