The Closeness function returns closeness and k-degree scores for each specified source vertex in a graph. The closeness scores are the inverse of the sum, the inverse of the average, and the sum of inverses for the shortest distances to all reachable target vertices (excluding the source vertex itself).The graph can be directed or undirected, weighted or unweighted.
For large graph, you can apply the function to a random sample of the specified target vertices to get an efficient approximation of the closeness and k-degree scores.
The Closeness function applies the classical definition of closeness to connected graphs and an alternative definition to disconnected graphs. The alternative definition that the function uses adds 0 to the sum for each unreachable target vertex, which is consistent with the classic definition, because the inverse distance is effectively 0 for a disconnected graph.
The Closeness function uses a hybrid distributed all pairs shortest path (APSP) algorithm to calculate the shortest distances from each specified source vertex to each specified target vertex and then aggregates these shortest distances into closeness and k-degree scores for each source vertex. By restricting the number of parallel single node shortest path (SNSP) executions to groups of P vertices, the APSP algorithm enables a trade-off between time and memory usage. The APSP algorithm completes when N/P of these groups have completed, where N is the number of vertices in the graph. (For more information, see AllPairsShortestPath (ML Engine).)