Degree-based entropy H_d(G) = -Σ (d(v)/2m)·log₂(d(v)/2m). Applies Shannon's information entropy to the degree sequence treated as a probability distribution. Dehmer (2008). Maximum entropy ↔ maximally irregular. Zero entropy ↔ regular.
How to Use
Select graph:
- H_d: Degree entropy
- p(v): d(v)/2m
- Bits: Information
Information View
Low H_d: predictable degrees (regular, few distinct values). High H_d: unpredictable degrees (many distinct values, spread out). H_d measures how much 'information' is in the degree sequence.
Bounds
0 ≤ H_d ≤ log₂(n). H_d = log₂(n) iff all p(v) equal iff regular n-regular. H_d near 0: nearly all degree concentrated in one vertex (star-like).
Step-by-Step Instructions
- 1Select graph.
- 2Compute p(v) = d(v)/2m.
- 3For each v: -p·log₂(p).
- 4Sum all terms.
- 5Compare with log₂(n).