Neighborhood degree sum S(v) = Σ d(u) for u ∈ N(v). How much total degree surrounds vertex v. Fundamental building block: many indices use S(v). Hub vertices surrounded by hubs have highest S(v). Identifies structurally critical vertices.
How to Use
Select graph:
- S(v): Per vertex
- Max S: Hub center
- ΣS: Graph total
Hub Detection
High S(v): v is surrounded by high-degree vertices. Maximum S identifies the 'center of connectivity'. For star: hub has S = n-1 (sum of leaf degrees=1 each), leaves have S = degree of hub.
Index Building Block
Many indices use S(v): neighborhood Zagreb = Σ S(v)². Neighborhood Randić = Σ 1/√(S(u)·S(v)) over edges. S(v) is the fundamental 'second-order' degree measure.
Step-by-Step Instructions
- 1Select graph.
- 2For each vertex: sum neighbor degrees.
- 3Identify max/min S(v).
- 4Compute graph-wide ΣS.
- 5Find hub centers.