Edge connectivity λ(G): minimum edges to remove to disconnect G. Whitney: κ ≤ λ ≤ δ. Menger (edge): max edge-disjoint u-v paths = min u-v edge cut. λ(K_n)=n-1, λ(K_{m,n})=min(m,n), λ(C_n)=2.
How to Use
Select graph:
- λ: Edge connectivity
- Bridge: λ=1 edge
- Whitney: κ ≤ λ ≤ δ
Max-Flow Connection
λ(G) = min over all pairs (u,v) of max-flow(u,v) with unit-capacity edges. By max-flow min-cut theorem, this equals the minimum edge cut. Can be computed in O(n) max-flow computations using Gomory-Hu tree.
Bridges
A bridge is an edge whose removal disconnects G (λ=1 locally). Found in O(n+m) by DFS. A graph is 2-edge-connected iff it has no bridges iff every edge lies on a cycle. Ear decomposition characterizes 2-edge-connected graphs.
Step-by-Step Instructions
- 1Select graph.
- 2Compute λ(G).
- 3Find bridges.
- 4Check Whitney.
- 5Compare κ,λ,δ.