[igraph] find weights along all paths between two vertices

[Ana Sofia Morais]

Dear all,

 

I need to calculate the sum of the weights along all paths from each of n-1vertices to a target vertex in a graph.

 

Example:

 

mat=matrix(c(rep(0,6),3,0,2,rep(0,3),4,rep(0,2),2,rep(0,6),rep(1,2),rep(0,2),3,rep(0,9)),byrow=T,ncol=6)

graph = graph.adjacency(mat, mode="directed", weighted=TRUE)#do graph

plot.igraph(graph,edge.label=E(graph)$weight)

 

Assuming that vertex 1 is the target, the sum of the weights (sw) along the paths from every other vertex in the graph should be:

 

sw_V2 = 3+2+4

sw_V3 = 4

sw_V4 = 1+3+4

sw_V5 = 3+4

sw_V6 = 0

 

Note that, in identifying all paths from a vertex to the target, only paths have been considered in which a vertex is traversed only once along the same path. This applies to vertex 5, for instance, where the sum of weights disregards the weights present in the cycle with vertices 3 and 4.

 

I would appreciate any advice about how this could be achieved. Thanks in advance,

 

Sofia