# Calculate the average distance over all pairs of nodes in a graph

How can one calculate the average distance on a graph with 5 nodes?
Is there a simple way to find the average?
Can some one share some examples?

Thanks

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What's the configuration of the graph? – Imray Jun 10 '14 at 8:16

If you have a graph on 5 nodes then you can probably calculate the distances between all the pairs of vertices manually and then divide the result by 10

If you happen to have a large graph you can construct the all pair distance matrix (using for example this algorithm) and then sum all the entries of the matrix and divide by the number of all pairs of vertices.

Additionally, if you happen to know the Wiener index of your graph you just divide the index by $n(n-1)$ where $n$ is the number of vertices of your graph.

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