Structural Transitions in Dense Networks
| Autor: | Lambiotte, R., Krapivsky, P. L., Bhat, U., Redner, S. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Phys. Rev. Lett. 117, 218301 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.117.218301 |
| Popis: | We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree increasing with number of nodes $N$) for $p\geq \frac{1}{2}$. In the dense regime, individual networks realizations built by this copying mechanism are disparate and not self-averaging. Further, there is an infinite sequence of structural anomalies at $p=\frac{2}{3}$, $\frac{3}{4}$, $\frac{4}{5}$, etc., where the dependences on $N$ of the number of triangles (3-cliques), 4-cliques, undergo phase transitions. When linking to second neighbors of the target can occur, the probability that the resulting graph is complete---where all nodes are connected---is non-zero as $N\to\infty$. Comment: 5 pages, 5 figures, revtex 2-column format |
| Databáze: | arXiv |
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