Mostar index Mo(G) = Σ |nᵤ(e)-nᵥ(e)| over edges. Named after the Stari Most (Old Bridge) in Mostar, Bosnia — symbolizing how each edge 'bridges' two sides. Mo = 0 iff graph is distance-balanced: every edge divides vertices equally.
How to Use
Select graph:
- Mo: Mostar index
- |n-n|: Per edge
- =0?: Distance-balanced
The Bridge Metaphor
Each edge is a 'bridge' between two communities. nᵤ = people on u's side. nᵥ = people on v's side. |nᵤ-nᵥ| = population imbalance. Total Mostar = total imbalance across all bridges.
Distance-Balanced
Mo = 0 ⟺ distance-balanced: for every edge (u,v), exactly half the vertices are closer to u, half to v. Examples: K_n, C_{2k}, hypercubes Q_k, Petersen graph.
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: |nᵤ-nᵥ|.
- 3Sum over edges.
- 4Check if Mo=0.
- 5Rank asymmetry.