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NETWORK > CENTRALITY > INFORMATION
PURPOSE Calculate the Stephenson and Zelen information centrality measure for each vertex, and give an overall network information centralization index.
DESCRIPTION The weighted function of the set of all paths connecting vertex i to vertex j is any weighted linear combination of the paths such that the sum of the weights is unity. Assuming that each link in a path is independent, and the variance of a single link is unity, it can be concluded that the variance of a path is simply its length.
The information measure between two vertices i and j is the inverse of the variance of the weighted function. The information centrality of a vertex i is the harmonic mean of all the information measures between i and all other vertices in the network.
The routine calculates these measures and some descriptive statistics based on these measures for symmetric graphs.
PARAMETERS
Input dataset:
Name of file containing network to be analyzed. Data type: Graph.
Include diagonal in calculations? (Default = NO).
If NO self-loops are ignored.
Output dataset: (Default = 'Information').
Name of file which will contain information content and normalized information centrality of each vertex.
LOG FILE A table which contains a list of the information content Together with descriptive statistics which give the mean, standard deviation, variance, minimum value and maximum value.
TIMING O(N^3).
COMMENTS None
REFERENCES Stephenson K and Zelen M (1991). 'Rethinking Centrality'. Social Networks 13.