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## Re: [igraph] Turn a directed network into a weighted undirected network

 From: MikeS Subject: Re: [igraph] Turn a directed network into a weighted undirected network Date: Tue, 7 Jun 2016 15:15:38 +0700

```Hello,

Tamas, thanks a lot.

I have used the your function.

In order to trace calculation step by step, I reduced the original
graph G, now it has only one triangle (type #2).

On the step # 2 I have found all triangles in the undirected graph.
There are k=6 subisomorphisms.

On the step # 3 I have found subisomorphisms in the directed graph to
all of the four templates.

> subisom
[[1]]
list()

[[2]]
[[2]][[1]]
+ 3/3 vertices, named:
[1] a b c

[[3]]
list()

[[4]]
list()

As can see only one list subisom[[2]][[1]] is not empty, and the index
of this list corresponds to the triangle type (type #2). This is the
weight for the triangle in the undirected graph.

I'm looking an idea for the function to check which template graph it
was isomorphic on the step #4:

function_check_which_template_graph_it_was_isomorphic(subisom[j],
sbg.triangle[i])

Could someone please give an idea how to check it?

library(igraph)
set.seed(42)

d <- matrix(c(0,1,0, 0,0,1, 1,1,0),nrow=3,ncol=3)
V(G)\$name <- letters[1:dim(d)[1]]
V(G)\$shape = "none"
plot(G, edge.arrow.size=0.5, edge.curved=TRUE)

# Here are the adjacency matrices for each of the four subgraphs

d0<-matrix(c(0,1,0,0,0,1,1,0,0),nrow=3,ncol=3)
d1<-matrix(c(0,1,0,0,0,1,1,1,0),nrow=3,ncol=3)
d2<-matrix(c(0,1,0,1,0,1,1,1,0),nrow=3,ncol=3)
d3<-matrix(c(0,1,1,1,0,1,1,1,0),nrow=3,ncol=3)

# Turn them into a convenient list

sbgCycle.mat<-list(d0,d1,d2,d3)
n <- length(list(d0,d1,d2,d3))

# And then into a list of graph objects

pattern <- lapply(sbgCycle.mat, graph.adjacency)

# 1. Convert the directed graph to undirected one

UG <- simplify(G)
UG <- as.undirected(UG)

# 2. Search for triangles in the undirected graph

triangle <- graph.full(3)
# names of incident vertices of triangle in the undirected graph
sbg.triangle <- unique(graph.get.subisomorphisms.vf2(UG, triangle))
k <- length(sbg.triangle)

vertices_of_triangle <- function (x) { c(x[1], x[2], x[2], x[3], x[3], x[1]) }
vlist <- lapply(1:k, function(x) vertices_of_triangle(sbg.triangle[[x]]) )

# edge IDs triangle in the undirected graph
eids <- lapply(1:k, function(x) get.edge.ids(graph = UG, vp =
as.numeric(unlist(vlist[x])) ))

# 3. Search for subisomorphisms in the directed graph to all of the
four templates

subisom <- lapply(1:n, function(x) subgraph_isomorphisms(pattern[[x]],

# 4. For each triangle check which pattern it was isomorphic

for(i in 1:k)
{
for(j in 1:n)
{
weght_triangle <-
function_check_which_template_graph_it_was_isomorphic(subisom[j],
sbg.triangle[i])
} # for_j

E(UG)[eids[k]]\$weght <- weght_triangle
} # for_i

plot(UG, edge.arrow.size=0.2, edge.label=E(UG)\$weght)

--
Mikes

```

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