EV-degree ev(e) = |N[u] ∪ N[v]| for edge e=(u,v). Counts vertices reachable within distance 1 from e. Dual of ve-degree. Chellali et al. (2017). ev(e) ≤ n always. ev(e) = n iff e is a dominating edge.
How to Use
Select graph:
- ev(e): Per edge
- Reach: Union size
- vs d+d: Compare
EV-Degree
ev(e=(u,v)) = |N[u] ∪ N[v]|. By inclusion-exclusion: ev(e) = d(u)+d(v)-|N(u)∩N(v)| (common neighbors subtracted). ev(e) = d(u)+d(v) iff no common neighbors.
Applications
ev(e) measures edge 'influence radius'. High ev: the edge reaches many vertices. Critical for epidemic spreading models: edges with high ev spread infections fastest.
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: N[u] ∪ N[v].
- 3Count union size.
- 4Compare across edges.
- 5Find dominating edges.