Graph resilience res(G): minimum over all vertices v of the local edge connectivity at v. Each vertex has a 'resilience' — how many of its incident edges must fail to isolate it. res(G) = the weakest vertex's resilience. res ≤ δ(G) ≤ λ(G).
How to Use
Select graph:
- res: Resilience
- Weakest: Min vertex
- Local λ: Per-vertex
Per-Vertex Analysis
Unlike global connectivity, resilience examines each vertex individually. The weakest vertex determines overall resilience. Identifies critical nodes that are easiest to isolate. Actionable for network hardening.
Network Hardening
Identify vertices with low local resilience. Add redundant edges to strengthen weak points. Cost-effective network improvement. Used in critical infrastructure protection.
Step-by-Step Instructions
- 1Select graph.
- 2Compute per-vertex λ.
- 3Find minimum.
- 4Identify weak vertex.
- 5Strengthen weakest.