Albertson index A(G) = Σ |dᵢ-dⱼ| over edges. Albertson (1997). The simplest irregularity measure: sum of absolute degree differences across edges. A = 0 ⟺ regular graph. Linear in degree gaps.
How to Use
Select graph:
- A: Albertson index
- |d-d|: Per edge
- A=0?: Regular
A vs σ
σ = Σ(dᵢ-dⱼ)² (squared differences). A = Σ|dᵢ-dⱼ| (absolute). σ penalizes large gaps more. A is linear. Both are zero iff regular. A² ≤ m·σ (Cauchy-Schwarz).
Bounds
0 ≤ A ≤ m(n-2). A(star) = (n-1)(n-2). For trees: A maximized by star. A/m = average edge imbalance.
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: |dᵢ-dⱼ|.
- 3Sum all terms.
- 4Check if A=0.
- 5Compare with σ.