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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.