A logical limit law for the sequential model of preferential attachment graphs
Abstract
For a sequence of random graphs, the limit law we refer to is the existence of a limiting probability of any graph property that can be expressed in terms of predicate logic. A zero-one limit law is shown by Shelah and Spencer for Erdös-Renyi graphs given that the connection rate has an irrational exponent. We show a limit law for preferential attachment graphs which admit a Pólya urn representation. The two extreme cases of the parametric model, the uniform attachment graph and the sequential Barabási-Albert model, are covered separately as they exhibit qualitative differences regarding the distribution of cycles of bounded length in the graph.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.07475
- arXiv:
- arXiv:2408.07475
- Bibcode:
- 2024arXiv240807475O
- Keywords:
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- Mathematics - Probability;
- Mathematics - Combinatorics;
- Mathematics - Logic
- E-Print:
- 42 pages