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Entropy of labeled versus unlabeled networks
Jeremy Paton1,2, Harrison Hartle2, Huck Stepanyants1,2
1Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.
Physical Review. E
|December 23, 2022
Summary
Meaningless node labeling in network models can obscure structural information. This study shows that in sparse networks, labeling entropy can outweigh network structure entropy, questioning current network science methods.
Area of Science:
- Network Science
- Statistical Physics
- Graph Theory
Background:
- Complex network models often use labeled graphs with arbitrary integers.
- The impact of this labeling on structural analysis is not well understood.
- Distinguishing between labeling noise and intrinsic network structure is crucial.
Purpose of the Study:
- To investigate whether meaningless graph labeling can dominate network structure.
- To compare the entropy of labeled and unlabeled versions of network models.
- To assess the implications for statistical network science methodologies.
Main Methods:
- Introduced sparse unlabeled versions of common network models.
- Compared the entropy of labeled and unlabeled graph models.
- Derived bounds for the entropy of labeled and unlabeled random geometric graphs.
Main Results:
- Erdős-Rényi graphs show entropic equivalence between labeled and unlabeled versions.
- Configuration models may exhibit differences in entropy prefactors.
- Unlabeled one-dimensional random geometric graphs have negligible entropy compared to labeled versions.
Conclusions:
- In sparse networks, labeling entropy can overpower network structure entropy.
- Using exchangeable models for distinguishable nodes may introduce significant biases.
- A reevaluation of the statistical foundations of network science is recommended.
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