Rupture degree r(G) = max_S (ω(G-S) - |S| - τ(G-S)). Refines scattering number by subtracting the largest remaining component. Accounts for: more pieces (good for attacker), fewer removals (cheaper attack), smaller remnant (more damage).
How to Use
Select graph:
- r: Rupture degree
- ω-|S|-τ: Formula
- vs sc: Compare
vs Scattering Number
Scattering: ω-|S|. Rupture: ω-|S|-τ. The extra -τ penalizes large surviving components. Even if many pieces, a large remnant means less damage. Rupture degree captures this.
Applications
Network vulnerability: how badly can an attacker fragment a network? Rupture degree considers both fragmentation count AND surviving functionality. More realistic than simple connectivity.
Step-by-Step Instructions
- 1Select graph.
- 2Find max ω-|S|-τ.
- 3Compare with sc.
- 4Assess vulnerability.
- 5Check bounds.