Graph theory (Diestel, 2005) is a branch of mathematics that allows one to explore the
topological properties of graphs. Graph-theoretic analyses have been used in
neuroscience for such purposes as investigating neural connectivity patterns (Sporns,
2002), correcting brain images (Han, et al. 2001), and analyzing the patterns of neural
activations in epilepsy (Suharitdamrong, Chaovalitwongse and Pardalos, 2006).
One of the simplest concepts in graph theory is minimum graph distance, which is just
the fewest number of edges one must traverse to get from one node to another. Nodes that
are adjacent in a graph have a graph distance of 1, nodes not adjacent to each other, but
both adjacent to a third have a graph distance of 2, and so on. The minimum graph
distance between every pair of nodes in the graph of the cortex was calculated using
Dijkstra’s algorithm (Dijkstra, 1959).
A simple extension of minimum graph distance is average minimum graph distance,
which is the average of the minimum graph distances between every pair of nodes in
some subset of nodes in a graph. Figure 1 illustrates some different graphs, and the
average minimum graph distances between all the nodes in the graph.
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