Edge Integrity Calculator

edge failure vulnerability

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About Edge Integrity Calculator

An edge integrity calculator computing EI(G) = min over edge subsets F of |F| + τ(G-F). Edge analogue of vertex integrity. Measures edge-failure vulnerability. EI ≥ λ+1. Lower EI = more fragile under edge attacks. Network link reliability. Client-side.

Edge Integrity Calculator Features

  • EI(G)
  • |F|+τ
  • vs I(G)
  • Edge analog
  • Common graphs
Edge integrity EI(G) = min_F (|F| + τ(G-F)) over edge subsets F. Edge analogue of vertex integrity. Balances: edges removed + largest surviving component. Low EI = network shatters easily under link failures.

How to Use

Select graph:

  • EI: Edge integrity
  • |F|+τ: Cost+remnant
  • vs I: Compare

Edge vs Vertex

Vertex integrity: remove vertices. Edge integrity: remove edges. Edge version models link failures (cable cuts, wireless interference). Often more practical for communication networks.

Bounds

EI ≥ λ+1 (edge connectivity + 1). EI ≤ n (remove nothing, τ = n). Trees: EI = ⌈(n+1)/2⌉ approximately. Complete: EI = n. Stars: EI = 2 (very fragile!).

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Find min |F|+τ.
  3. 3Compare with I(G).
  4. 4Check bounds.
  5. 5Assess link resilience.

Edge Integrity Calculator — Frequently Asked Questions

How does edge integrity compare to vertex integrity?+

Same concept, different failure mode. Vertex integrity removes nodes; edge integrity removes links. EI is typically larger than or equal to I for the same graph since edge removal is less destructive.

Why is star's EI = 2?+

Remove all edges from one leaf (|F|=1), largest component has 1 fewer vertex but center keeps most. Actually: remove 0 edges, τ = n. But remove n-1 edges (all from center): τ=1, EI = n-1+1 = n. Optimal: EI = 2 comes from specific cuts.

Applications?+

Fiber optic networks: cable cuts. Wireless: link interference. Power grids: transmission line failures. Internet: routing link outages. All model edge failures naturally.

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