Degree power sum Σ d(v)^k. The most general vertex-based degree invariant. k=0:n. k=1:2m. k=2:M₁. k=3:F. k=-1:ID. k=-2:mM₁. One formula, one slider, infinite indices. The 'periodic table' of vertex degree indices.
How to Use
Select graph and k:
- k=2: M₁
- k=3: F
- k=-1: ID
Unification
All vertex-based degree indices are special cases of Σd^k. Positive k → hub emphasis. Negative k → leaf emphasis. k=0 → neutral (just vertex count). The sign of k determines the structural focus.
Statistical Moments
Σd^k/n = k-th moment of degree distribution (when appropriately normalized). M₁/n = second moment. F/n = third moment. Bell variance = M₁/n - (2m/n)². Pure statistics!
Step-by-Step Instructions
- 1Select graph.
- 2Choose exponent k.
- 3For each vertex: d(v)^k.
- 4Sum all terms.
- 5Identify the named index.