Finding all triangles in a graph

I have the adjacency matrix of a graph. I'm trying to find all
triangles (embeddings of C_3). This doesn't work:

index = function(l) seq(l)[l]
pairs = do.call(rbind, lapply(seq(nrow(adj)), function(x) cbind(x,
index(adj[x,]))))
triangles = do.call(rbind, apply(pairs, 1, function(x) cbind(x,
index(adj[x[1],] & adj[x[2],]))))

I'm absolutely certain I've gone down the wrong path here. O great R
gurus, your guidance would be most welcome.

Taral <taralx at gmail.com>
"Please let me know if there's any further trouble I can give you."
? ? -- Unknown