Convert adjacency (or other) matrix to edge list

example.R

library(reshape2)

gen.mat.to.edge.list<-function(mat,symmetric=TRUE,diagonal=FALSE,text=FALSE){
	#create edge list from matrix
	# if symmetric duplicates are removed
	mat<-as.matrix(mat)
	id<-is.na(mat) # used to allow missing
	mat[id]<-"nna"
	if(symmetric){mat[lower.tri(mat)]<-"na"} # use to allow missing values
	if(!diagonal){diag(mat)<-"na"}
	obj<-melt(mat)
	colnames(obj)<-c("source","target","value")
	obj<-obj[!obj$value=="na",]
	obj$value[obj$value=="nna"]<-NA
	if(!text){obj$value<-as.numeric(as.character(obj$value))}
	return(obj)
	# remove duplicates
}	

#example 
R-3.1.2> x<-matrix(1:6,3,3)
R-3.1.2> x
     [,1] [,2] [,3]
[1,]    1    4    1
[2,]    2    5    2
[3,]    3    6    3

#if matrix is symmetric it extracts one of the triangles (here top)
R-3.1.2> gen.mat.to.edge.list(x)
  source target value
4      1      2     4
7      1      3     1
8      2      3     2

If not symmetric and you want diagonal then do the following:
R-3.1.2> gen.mat.to.edge.list(x,symmetric=FALSE,diagonal = TRUE)
  source target value
1      1      1     1
2      2      1     2
3      3      1     3
4      1      2     4
5      2      2     5
6      3      2     6
7      1      3     1
8      2      3     2
9      3      3     3

#with mising values present 
R-3.1.2> x[sample(1:6,3)]<-NA
R-3.1.2> x
     [,1] [,2] [,3]
[1,]    1   NA    1
[2,]    2    5    2
[3,]   NA   NA    3

R-3.1.2> gen.mat.to.edge.list(x,symmetric=FALSE,diagonal = TRUE)
  source target value
1      1      1     1
2      2      1     2
3      3      1    NA
4      1      2    NA
5      2      2     5
6      3      2    NA
7      1      3     1
8      2      3     2
9      3      3     3