KEdgeConnectedGraphQ
KEdgeConnectedGraphQ[g,k] yields True if the graph g is k-edge-connected and False otherwise.
Examples
Check if a graph is 2-edge-connected:
KEdgeConnectedGraphQ[CompleteGraph[5], 2]
(* True *)KEdgeConnectedGraphQ[PathGraph[{1, 2, 3}], 2]
(* False *)Please visit the official Wolfram Language Reference for more details.