How can I get a correlogram for spatial autocorrelation in networks in R?

Question

I would like to see if there's spatial autocorrelation of a measured y for the vertices of my network. The vertices are somewhat clustered. Non-connected vertices I assume to be independent. So essentially it's autocorrelation on a cluster basis (ideally also for all clusters seperately, because for the clusters the degree of autocorrelation might be very different.

Here's what I've done so far:

library(statnet)
library(ncf)
data <- data.frame("id" = 1:100, "cluster" = c(rep(1:7, each = 10), 8:37), "y" = rnorm(100, 0, 1))
grid <- expand.grid(1:100, 1:100)
grid$overlap <- ifelse(data$cluster[grid$Var1] == data$cluster[grid$Var2], 1, 0)
grid$overlap[grid$overlap == 1] <- unlist(lapply(grid$overlap[grid$overlap == 1],
  function(x)
    ifelse(runif(1, 0, 100) < (.5 / 2 * 100), 1, 0)))
connect_mat <- matrix(data = grid$overlap, nrow = 100, ncol = 100, byrow = T)
net <- as.network(connect_mat, directed = F)
coord_net <- gplot(net, gmode = "graph")
corlog <- correlog(coord_net[, 1], coord_net[, 2], paper$effect, increment = 1)
plot(corlog)

Example network Correlogram of example network

This is just for illustrating what I want, here I of course don't expect any autocorrelation. For now I have used the coordinates of the vertices in the network plot to look at autocorrelation. There are a few reasons I don't want to do this:

1. Every time I run the "coord_net" line the coordinates change. This wouldn't matter if the distances between vertices remained the same but I don't think they do.
2. Marginal vertices might be closer to isolates than to distant members of their respective cluster.
3. The x axis in the correlogram is not really intuitive (at least for me) and doesn't take into account the network structure appropriately.

These points could (hopefully) all be fixed if I, instead of the coordinates, used the geodesic distances between vertices (i.e. how many steps do I need to get from one vertice to another). So all members of the same cluster would have distances from 1 to 5 roughly and Inf to all others.

Soo my question is essentially: Is there a way to give correlog a distance matrix (that involves Inf) instead of x and y coordinates? Or maybe a better way of using the coordinates that returns consistent results and includes the clustering of the network?