# Third mini-project: Edge-connectivity in graphs solution

I. MEASURES OF CONNECTIVITY A measure of the robustness of a network is the number of edges whose failure prevents network-wide communications. A network is modeled as a graph. The edge-connectivity of a network is the minimum size of a set of edges the removal of which prevents the network from being connected. The edge-connectivity of a network is a global parameter. In order to compute the edge-connectivity of a network, we may start by analyzing the edge-connectivity between pairs of nodes. Oftentimes, the edge-connectivity between pairs of nodes is interesting in its own right. A set of edges separates a source node from a destination node if every path from the source to the destination contains at least one edge belonging the set. It is well-known that the minimum number of edges that separates a source node from a destination node equals the maximum number of edge-disjoint paths from the source to the destination. A set of paths is edge-disjoint if the paths do not share an edge.