* Why do you want to base this on Dijkstra's algorithm, which is designed to find a single shortest-path? Surely there are better options for your base implementation. A quick Google search suggests a ...

Let G = (V(G), E(G)) be a graph. A set S ⊆ E(G) is an edge k-cut in G if the graph G − S = (V(G), E(G) \ S) has at least k connected components. The generalized k-edge connectivity of a graph G, ...