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Some more network theory concepts that might be useful in brain connectivity analysis (most of them collected from BCT, sporns et al):
Shorcuts: are central edges which significantly reduce the characteristic path length in the network
The characteristic path length is the average shortest path length in the network.
The global efficiency is the average inverse shortest path length in the network.
The eccentricity of a graph vertex v in a connected graph G is the maximum graph distance between v and any other vertex u of G. For a disconnected graph, all vertices are defined to have infinite eccentricity.
Graph diameter: The maximum eccentricity is the graph diameter.
Graph radius: The minimum graph eccentricity is called the graph radius.
The assortativity coefficient is a correlation coefficient between the degrees of all nodes on two opposite ends of a link. A positive assortativity coefficient indicates that nodes tend to link to other nodes with the same or similar degree.
The global efficiency is the average of inverse shortest path length, and is inversely related to the characteristic path length.The local efficiency is the global efficiency computed on the neighborhood of the node, and is related to the clustering coefficient.
Transitivity is the ratio of 'triangles to triplets' in the network (A classical version of the clustering coefficient).
Matching index: For any two nodes u and v, the matching index computes the amount of overlap in the connection patterns of u and v. Self-connections and u-v connections are ignored. The matching index is a symmetric quantity, similar to a correlation or a dot product.
The optimal community structure is a subdivision of the network into nonoverlapping groups of nodes in a way that maximizes the number of within-group edges, and minimizes the number of between-group edges.
The modularity is a statistic that quantifies the degree to which the network may be subdivided into such clearly delineated groups.
Participation coefficient is a measure of diversity of intermodular connections of individual nodes.The within-module degree z-score is a within-module version of degree centrality.
Closeness centrality: In the network theory, closeness is a sophisticated measure of centrality. It is defined as the mean geodesic distance (i.e., the shortest path) between a vertex v and all other vertices reachable from it:
CC=\frac{\Sigma_{t \in V\\v}d_G(v,t)}{n-1}
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