Connectivity transitions in networks with super-linear preferential attachment
| dc.creator | Oliveira, Roberto | |
| dc.creator | Spencer, Joel | |
| dc.date | 2005-10-20 | |
| dc.date.accessioned | 2026-07-07T06:47:44Z | |
| dc.date.available | 2026-07-07T06:47:44Z | |
| dc.description | We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the p-th power of the in-degree of b. We restrict to the super-linear case p>1. When 1+1/k< p \leq 1 + 1/(k-1) the structure of the final countable tree is determined. There is a finite tree T with distinguished v (which has a limiting distribution) on which is "glued" a specific infinite tree. v has an infinite number of children, an infinite number of which have k-1 children, and there are only a finite number of nodes (possibly only v) with k or more children. Our basic technique is to embed the discrete process in a continuous time process using exponential random variables, a technique that has previously been employed in the study of balls-in-bins processes with feedback. | |
| dc.description | 43 pages, 2 figures. To appear in "Internet Mathematics" | |
| dc.identifier | https://arxiv.org/abs/math/0510446 | |
| dc.identifier | http://arxiv.org/abs/math/0510446 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103752 | |
| dc.subject | Probability | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Combinatorics | |
| dc.subject | 60C05,60J05,60J80,05C05,05C80 | |
| dc.title | Connectivity transitions in networks with super-linear preferential attachment | |
| dc.type | text |