Minimum Cost Flow - network optimization in R

Question

I am trying to implement a \"Minimum Cost Network Flow\" transportation problem solution in R.

I understand that this could be implemented from scratch

Answer 1

I was looking for a function but didn't success. The original function calls another: res <- .Call("R_igraph_maxflow", graph, source - 1, target - 1, capacity, PACKAGE = "igraph")

And I don't know how to deal with it.

For the moment I inverted the cost path values in order to use the same function in oposite direction:

E2 <- E # create another table
E2[, 3] <- max(E2[, 3]) + 1 - E2[, 3] # invert values

E2
     from to capacity
[1,]    1  3        8
[2,]    3  4       10
[3,]    4  2        9
[4,]    1  5       10
[5,]    5  6        9
[6,]    6  2        1

g2 <- graph_from_data_frame(as.data.frame(E2)) # create 2nd graph

# Get maximum flow
m1 <- max_flow(g1, source=V(g1)["1"], target=V(g1)["2"])
m2 <- max_flow(g2, source=V(g2)["1"], target=V(g2)["2"])

m1$partition2 # Route on maximal cost
+ 4/6 vertices, named:
[1] 4 5 6 2

m2$partition2 # Route on minimal cost
+ 3/6 vertices, named:
[1] 3 4 2

I draw in paper the graph and my code agree with manual solution This method should be tested with real know values, as I mentioned in the comment