You can weight to your graph like this:
Example:
gg3 <- graph.ring(10)
[1,] . 1 . . . . . . . 1
[2,] 1 . 1 . . . . . . .
[3,] . 1 . 1 . . . . . .
[4,] . . 1 . 1 . . . . .
[5,] . . . 1 . 1 . . . .
[6,] . . . . 1 . 1 . . .
[7,] . . . . . 1 . 1 . .
[8,] . . . . . . 1 . 1 .
[9,] . . . . . . . 1 . 1
[10,] 1 . . . . . . . 1 .
E(gg3)$weight <- 15
[1,] . 15 . . . . . . . 15
[2,] 15 . 15 . . . . . . .
[3,] . 15 . 15 . . . . . .
[4,] . . 15 . 15 . . . . .
[5,] . . . 15 . 15 . . . .
[6,] . . . . 15 . 15 . . .
[7,] . . . . . 15 . 15 . .
[8,] . . . . . . 15 . 15 .
[9,] . . . . . . . 15 . 15
[10,] 15 . . . . . . . 15 .
or
E(gg3)$weight <- c(20,10)
[1,] . 20 . . . . . . . 10
[2,] 20 . 10 . . . . . . .
[3,] . 10 . 20 . . . . . .
[4,] . . 20 . 10 . . . . .
[5,] . . . 10 . 20 . . . .
[6,] . . . . 20 . 10 . . .
[7,] . . . . . 10 . 20 . .
[8,] . . . . . . 20 . 10 .
[9,] . . . . . . . 10 . 20
[10,] 10 . . . . . . . 20 .
Check this out:
Using edge-lists with associated edge values to create a weighted network.