How can I calculate jaccard vertex similarity with weights in igraph - r

Question

I have a square matrix that represents directed interactions, with values representing the magnitude of the "flow" from row i to column j.
mat <- structure(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.59734154600838,
0.962276996464401, 0.996554553573577, 0.988150008522967, 0.581536975261071,
0.280105566896129, 0.0520717823071291, 0.0443864046117343, 0.0162858335588474,
0, 0, 0, 0, 0, 0, 0, 0.111900863185923, 0.289483837277475, 0.338036619790556,
0.973201117894343, 0.876145758734938, 0.280105566896129, 0.245172586054694,
0.101440228047504, 0.0136022221272776, 0, 0, 0, 0, 0, 0, 0.073088274682518,
0.21588462733217, 0.258134862678946, 0.93528472971792, 0.921844796228768,
0.318790697187933, 0.280105566896129, 0.117928032625428, 0.016073037487081,
0, 0, 0, 0, 0, 0, 0, 0.0119602547215087, 0.0174757225504163,
0.443466799224191, 0.941024455005652, 0.632609306727839, 0.57418820480725,
0.280105566896129, 0.043827579210664, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0.0547471528159807, 0.884304818335752, 0.937495721370637,
0.925118019265575, 0.280105566896129, 0.055967839940851, 0.0122649398400715,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0679263578760456, 0.104884821422108,
0.569814755335506, 0.853130344409379, 0.280105566896129, 0.0728699300735904,
0.0339371561178606, 0.012188886551821, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0.0219303360220489, 0.843994038605239, 0.759918325154657,
0.280105566896129, 0.143508732965731, 0.0556400089034765, 0.0296286033644999,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0.421151438381493, 0.977746695038157,
0.499880491267235, 0.280105566896129, 0.116686808742586, 0.0639605586005988,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0495967410949283, 0.841406989124245,
0.85505217514437, 0.578265483357174, 0.280105566896129, 0.163154497800251,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.499941945587477, 0.993657104473566,
0.807475685951474, 0.45318772928331, 0.280105566896129), .Dim = c(15L,
15L))
I am interested in calculating the weighted linkage similarity (both in and out flows) of all vertices in the network, so taking magnitude into account.
Using igraph, I can calculate the Jaccard similarity but without considering weights
library(igraph)
bin <- mat
bin[bin > 0] <- 1
similarity(graph_from_adjacency_matrix(bin),
mode = "all",
method = "jaccard")
# this gives the same result as the one above
similarity(graph_from_adjacency_matrix(mat, weighted = T),
mode = "all",
method = "jaccard")
Using the code from this blogpost, I was able to calculate the Jaccard similarity of outflows and inflows and combine them.
# outflow similarity
sim.jac.out <- matrix(0, nrow=nrow(mat), ncol=nrow(mat))
pairs <- t(combn(1:nrow(mat), 2))
for (i in 1:nrow(pairs)) {
num <- sum(sapply(1:ncol(mat), function(x) (min(mat[pairs[i,1],x], mat[pairs[i,2],x]))))
den <- sum(sapply(1:ncol(mat), function(x) (max(mat[pairs[i,1],x], mat[pairs[i,2],x]))))
sim.jac.out[pairs[i,1],pairs[i,2]] <- num/den
sim.jac.out[pairs[i,2],pairs[i,1]] <- num/den
}
sim.jac.out[which(is.na(sim.jac.out))] <- 0
diag(sim.jac.out) <- 1
# inflow similarity
sim.jac.in <- matrix(0, nrow=nrow(mat), ncol=nrow(mat))
pairs <- t(combn(1:nrow(t(mat)), 2))
for (i in 1:nrow(pairs)) {
num <- sum(sapply(1:ncol(t(mat)), function(x) (min(t(mat)[pairs[i,1],x], t(mat)[pairs[i,2],x]))))
den <- sum(sapply(1:ncol(t(mat)), function(x) (max(t(mat)[pairs[i,1],x], t(mat)[pairs[i,2],x]))))
sim.jac.in[pairs[i,1],pairs[i,2]] <- num/den
sim.jac.in[pairs[i,2],pairs[i,1]] <- num/den
}
sim.jac.in[which(is.na(sim.jac.in))] <- 0
diag(sim.jac.in) <- 1
# total similariry
sim.jac.all <- (sim.jac.in + sim.jac.out)/2
So the general question is, does this make sense?
But more specifically, I would be interested to know if there is a way to incorporate link weights in the calculation of similarity with igraph.
In my real dataset, I need to do this several times iteratively (swapping individuals), for a large number of networks, so my method would take forever. I believe igraph uses C++ under the hood.