Graph Entropy Calculator

structural information measure

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About Graph Entropy Calculator

A graph entropy calculator computing information-theoretic measures of graph structure. Includes degree-based entropy H_d = -Σ (d_i/2m) log(d_i/2m), von Neumann entropy from Laplacian spectrum, and chromatic entropy. Measures structural randomness. Client-side.

Graph Entropy Calculator Features

  • H_d degree
  • Von Neumann
  • Chromatic
  • Complexity
  • Common graphs
Graph entropy: information-theoretic quantification of graph structure. Degree entropy: H_d = -Σ (d_i/2m) log₂(d_i/2m). Measures degree heterogeneity. Von Neumann entropy: from normalized Laplacian eigenvalues. Multiple entropy measures capture different aspects.

How to Use

Select graph:

  • H_d: Degree entropy
  • H_vN: Von Neumann
  • Compare: Measures

Degree Entropy

H_d = -Σᵢ (dᵢ/2m) log₂(dᵢ/2m). Maximum for regular graphs (uniform distribution). Minimum for stars (one high-degree vertex). Measures how 'regular' or 'heterogeneous' the degree distribution is.

Applications

Network complexity: comparing brain networks, social networks. Chemistry: molecular complexity measures. Biology: protein interaction network diversity. Anomaly detection: entropy changes signal structural shifts.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Compute degree entropy.
  3. 3Compute von Neumann.
  4. 4Compare measures.
  5. 5Interpret complexity.

Graph Entropy Calculator — Frequently Asked Questions

What does graph entropy measure?+

Structural complexity/randomness. High entropy: uniform, random-like structure. Low entropy: ordered, predictable structure. Different entropy measures capture different aspects: degree distribution, spectral properties, coloring.

What's von Neumann entropy for graphs?+

S = -Tr(ρ log₂ ρ) where ρ = L̃/n (normalized Laplacian divided by n). Treats graph as quantum state. Captures spectral complexity. Maximum for complete graph, minimum for disconnected/star.

How is entropy used in network analysis?+

Comparing networks: similar entropy → similar complexity. Temporal networks: entropy change signals phase transitions. Community detection: minimize within-community entropy. Feature engineering for ML on graphs.

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