Graph Connectivity Theorem

The Graph Connectivity Theorem states that in a connected undirected graph, the minimum number of edges that need to be removed to disconnect the graph (called the edge connectivity) equals the smallest number of edges crossing any cut that separates the graph into two parts. Essentially, it links the idea of how resilient a network is to edge removal with the smallest "bottleneck" that divides the network, highlighting the relationship between the overall connectivity and the tightest point that holds the network together.