Neighbor connectivity κ_N(G): find S ⊆ V such that removing N[S] (closed neighborhood) disconnects G, minimizing |N[S]|. Models attacks that take out a node and all its neighbors (blast radius). κ_N ≤ κ always.
How to Use
Select graph:
- κ_N: Nbr. conn.
- N[S]: Blast radius
- vs κ: Compare
Blast Radius Model
When a node fails, it often takes down its neighbors too (power cascade, virus spread, blast wave). Neighbor connectivity models this cascade: removing S removes N[S]. More realistic failure model.
Computing κ_N
Check all subsets S (expensive!). For each S: remove N[S] and check connectivity. Finding min |N[S]| that disconnects. Polynomial for special classes. Related to domination and covering problems.
Step-by-Step Instructions
- 1Select graph.
- 2Find optimal S.
- 3Compute |N[S]|.
- 4Check disconnection.
- 5Compare with κ.