Here's the example might help you...
edges = {UndirectedEdge[1, 2], UndirectedEdge[1, 2], UndirectedEdge[2, 3],
UndirectedEdge[2, 3], UndirectedEdge[3, 4], UndirectedEdge[3, 4],
UndirectedEdge[3, 4], UndirectedEdge[1, 5], UndirectedEdge[1, 5],
UndirectedEdge[1, 5], UndirectedEdge[1, 5], UndirectedEdge[5, 6],
UndirectedEdge[5, 6], UndirectedEdge[2, 6], UndirectedEdge[6, 4],
UndirectedEdge[6, 4], UndirectedEdge[6, 4], UndirectedEdge[2, 5],
UndirectedEdge[2, 5], UndirectedEdge[3, 6]};
{nedges, weights} = Transpose[Tally[edges]];
g = Graph[nedges, EdgeWeight -> weights,
VertexLabels -> Placed["Name", Center], EdgeLabels -> "EdgeWeight",
VertexSize -> .2]
EdgeConnectivity[g]