On the Evolution of Random Graphs.¶
Erdős, P., & Rényi, A. (1960). On the Evolution of Random Graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 5, 17-61.
Cited by¶
4 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Criticality
- At criticality, the component-size distribution is a power law \(P(s) \propto s^{-5/2}\), the correlation length (typical finite-component size) diverges, and small edge additions produce disproportionately large changes — a transition Erdős and Rényi (1960) characterized in their original paper on random graph evolution.
This sourceSeminal characterization of the random-graph G(n,p) phase transition at mean degree one, where a giant connected component emerges, supporting the marker's percolation-criticality example.
- At criticality, the component-size distribution is a power law \(P(s) \propto s^{-5/2}\), the correlation length (typical finite-component size) diverges, and small edge additions produce disproportionately large changes — a transition Erdős and Rényi (1960) characterized in their original paper on random graph evolution.
- Percolation
- The Erdős-Rényi giant-component transition, carried over to internet topology, produces the robust-to-random-fragile-to-targeted result directly.
This sourceEstablishes the sudden emergence of a giant connected component in random graphs as edge density crosses a critical value.
- The Erdős-Rényi giant-component transition, carried over to internet topology, produces the robust-to-random-fragile-to-targeted result directly.
Domain-specific¶
- Local World Evolving Network Models
- Local-world models relax global-information assumptions in preferential attachment by giving arriving nodes access only to a sampled neighborhood, community, or bounded subset.
This sourceMath. Inst. Hung. Acad. Sci, Vol.5, p.17-61.
- Local-world models relax global-information assumptions in preferential attachment by giving arriving nodes access only to a sampled neighborhood, community, or bounded subset.
Mechanisms¶
- Component-Merge Simulation
- Across those runs it locates the point at which a giant component emerges — the percolation-style threshold
This sourceErdős and Rényi establish a threshold regime for the emergence of a giant component in an evolving random graph. They do not describe this mechanism's simulation runs, uncertainty bands, or candidate scoring rule.
- Across those runs it locates the point at which a giant component emerges — the percolation-style threshold
Verification¶
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Links previously used in the corpus¶
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