Misbalance Rodeg Calculator

weighted degree-difference irregularity

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About Misbalance Rodeg Calculator

A misbalance rodeg calculator computing MBrodeg(G) = Σ |d(i)-d(j)|·d(i)·d(j) over all edges. Combines irregularity (|d-d|) with multiplicative weight (dd). MBrodeg = 0 iff regular. Weighted irregularity measure. Client-side.

Misbalance Rodeg Calculator Features

  • MBrodeg
  • |d-d|·dd
  • Weighted A
  • MBrodeg=0↔reg.
  • Common graphs
Misbalance rodeg MBrodeg(G) = Σ |dᵢ-dⱼ|·dᵢ·dⱼ over edges. Weighted Albertson: multiplies degree difference by degree product. High-degree mismatched edges contribute more. MBrodeg = 0 ↔ regular.

How to Use

Select graph:

  • MBrodeg: Weighted irreg.
  • |d-d|·dd: Per edge
  • vs A: Compare

Weight Effect

Albertson A = Σ|d-d| weights all edges equally. MBrodeg = Σ|d-d|·dd weights by degree product. Hub-hub edges with mismatched degrees contribute most. More structurally relevant.

Bounds

0 ≤ MBrodeg. MBrodeg = 0 iff regular. For star K_{1,n-1}: MBrodeg = (n-1)·(n-2)·(n-1) = (n-1)²(n-2).

Step-by-Step Instructions

  1. 1Select graph.
  2. 2For each edge: |dᵢ-dⱼ|·dᵢ·dⱼ.
  3. 3Sum all terms.
  4. 4Check if = 0.
  5. 5Compare with A.

Misbalance Rodeg Calculator — Frequently Asked Questions

MBrodeg vs A?+

A = Σ|d-d| (unweighted). MBrodeg = Σ|d-d|·dd (weighted). MBrodeg amplifies irregular edges between high-degree vertices. A treats all edges equally.

MBrodeg vs σ?+

σ = Σ(d-d)² (squared, unweighted). MBrodeg = Σ|d-d|·dd (absolute, weighted). Different penalization and different weighting. Complementary measures.

For star graph?+

All edges have |d-d| = n-2, dd = n-1. So MBrodeg = (n-1)·(n-2)·(n-1) = (n-1)²(n-2). Grows cubically — faster than A = (n-1)(n-2).

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