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**NETWORK > CENTRALITY > PROXIMAL BETWEENNESS**

**PURPOSE **Calculates the proximal betweennes centrality of each vertex.

**DESCRIPTION **Let bjk be the proportion of all geodesics linking vertex j and vertex k which pass through vertex i where i is the penultimate vertex on the geodesic, that is (i,k ) is the last edge of the geodesic path The proximal betweenness of vertex i is the sum of all bjk where i, j and k are distinct. Proximal betweenness is therefore a measure of the number of times a vertex occurs in a penultimate position on a geodesic. The routine allows the user to include geodesics of length one, this is equivalent to adding the out-degree to each score or removing the restriction that j is distinct from i.

**PARAMETERS**

**Input Network Dataset:**

** **Name of file containing network to be analyzed. Data type: Digraph.

**Output Dataset: **(Default = <filename>-ProxBet).

Name of file which will contain the proximal betweenness centrality of each vertex.

**Include out-degree**

** **Checking the box will add the out-degree to all of the scores. This is equivalent to removing the restriction that j is distinct from i.

**LOG FILE ** A table which contains a list of the proximal-betweenness score for each vertex.

**TIMING** O(N^3).

**COMMENTS **None

**REFERENCES** None