EdgeIndex

EdgeIndex[g, e] gives the integer index for the edge e in the graph g.

Examples

Get edge index:

g = Graph[{a -> b, b -> c, c -> d}];
EdgeIndex[g, b -> c]
(* 2 *)

Use with edge list:

EdgeIndex[CompleteGraph[4], 1 <-> 3]

Please visit the official Wolfram Language Reference for more details.