VE-degree ve(v) counts edges in the closed neighborhood N[v]. For simple graphs: ve(v) = ½Σ_{u∈N[v]} d(u). Chellali et al. (2017). Related to but distinct from standard degree. ve-degree Zagreb indices use ve(v) in place of d(v).
How to Use
Select graph:
- ve(v): Per vertex
- ve vs d: Compare
- ve-M₁: Zagreb
VE-Degree
ve(v) = number of edges incident to at least one vertex in N[v] (closed neighborhood). Counts edges 'visible' from v. Always ve(v) ≥ d(v). For K_n: ve(v) = n(n-1)/2.
VE-Zagreb
ve-M₁ = Σ ve(v)². ve-M₂ = Σ_{edges} ve(u)·ve(v). Natural extensions of classical Zagreb using the richer ve-degree measure.
Step-by-Step Instructions
- 1Select graph.
- 2For each v: count edges in N[v].
- 3Get ve(v) per vertex.
- 4Compute ve-Zagreb.
- 5Compare with d(v).