Cross-closeness

Measure of vertical proximity (siblings, cousins) in a directed graph.

Standard centrality measures are for horizontal distance. On a directed graph, outcloseness measures ancestry and incloseness measures descent. Cross-closeness measures vertical distances, that is, shared ancestry.

There are three functions.

Crosscloseness.m returns the average cross-closeness of all nodes to selected nodes in a graph. The average is the generalized average for parameter h. If h=1, this is the arithmatic average, if h=-1, it is the harmonic average.

The other two are support functions.

Crossdistance.m returns the matrix of distances between all nodes.

Horzdist.m returns the distance between two nodes. Parameter d sets the depth: for d=1, only siblings are considered. For d=2, siblings and first cousins are considered. And so on.