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NETWORK>COHESION>GEODESIC CUBE

PURPOSE Constructs a three dimensional matrix based on the proportion of geodesics between all pairs of vertices that go through each vertex. The three dimensional matrix can be thought of as a collection of n separate nxn matrices one matrix for each vertex. The ith matrix details the proportion of geodesics between every pair of nodes that involve i. 

DESCRIPTION For each vertex i and every pair of vertices j and k let bijk be the proportion of geodesics connecting j and k that pass through i. Hence for a directed graph the sum of all the entries for a fixed i will be the unormalized betweenness score for i. For an undirected graph it will be twice the betweenness scores. The matrix shows for every node the extent to which it is in control of the geodesics between all pairs of other nodes. This matrix can be used for example to calculate the betweenness scores between specific nodes or types of nodes rather than looking at all nodes.

PARAMETERS
Input Network
Name of file containing dataset to be analyzed. Data type: Digraph.
    
Output Network
Name of file containing three dimensional cube with each vertx in a different level. Default <inputfilename>-gCube


LOG FILE Three dimensional matrix with entries of bijk with bjk shown as a two dimensional matrix for each i

TIMING O(N^4)

COMMENTS None

REFERENCES None