# Name for a property in graph theory

I'm using a measure in my graph analysis application and I'm unsure how to properly name it.

The measure is calculated separately for each node and represents a total number of pairs of nodes which have a shortest path going through that node.

I know it has similarity to a measure called betweenness, though this one is slightly different.

Is there a defined name for this sort of measure? If not, can someone suggest a good name for it?

Edit: The graph in question is unweighted

• "Shortest" compared to every edge in the graph, or just for the edges intersecting a particular vertex in question? – David G. Stork Nov 21 '17 at 18:28
• For each pair of nodes, it contributes $1$ instead of the number of shortest paths in your measure? – PSPACEhard Nov 22 '17 at 5:38
• How's that different from betweenness? – Ivan Neretin Nov 22 '17 at 7:38