The R igraph help for vertex.connectivity claims that "The maximum number of
vertex disjoint paths between two vertices is the same as their vertex
connectivity". However, this is true only if the two vertices are not linked by
an edge. Here is a short example:
> g = graph(c(0,1), dir=FALSE)
> g
Vertices: 2
Edges: 1
Directed: FALSE
Edges:
e
e [0] 0 -- 1
> vertex.connectivity(g, 0, 1)
Errore in vertex.connectivity(g, 0, 1) :
At flow.c:994 : vertices connected, Invalid value
> vertex.disjoint.paths(g, 0, 1)
[1] 1
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