Reverse Wiener Λ(G) = Σ [diam - d(i,j)]. Flips Wiener: close vertices contribute more. Λ + W = diam·C(n,2). Λ(K_n) = 0 (all distances = diam = 1). High Λ = many close pairs despite large diameter.
How to Use
Select graph:
- Λ: Reverse Wiener
- diam−d: Per pair
- Λ+W: Verify
W Complement
Λ + W = diam·n(n-1)/2. If you know W and diam, you get Λ for free. Λ measures 'closeness excess': how much closer pairs are than the worst case (diameter).
Bounds
Λ(K_n) = 0. Λ(P_n) = maximum among trees. Λ ≥ 0 always. For d-regular: Λ depends on diameter and distance distribution.
Step-by-Step Instructions
- 1Select graph.
- 2Find diameter.
- 3For each pair: diam - d(i,j).
- 4Sum all terms.
- 5Verify Λ+W.