On the evolution of scale-free graphs
| dc.creator | Lee, D. -S. | |
| dc.creator | Goh, K. -I. | |
| dc.creator | Kahng, B. | |
| dc.creator | Kim, D. | |
| dc.date | 2003-12-13 | |
| dc.date | 2003-12-23 | |
| dc.date.accessioned | 2026-07-07T02:55:23Z | |
| dc.date.available | 2026-07-07T02:55:23Z | |
| dc.description | We study the evolution of random graphs where edges are added one by one between pairs of weighted vertices so that resulting graphs are scale-free with the degree exponent $γ$. We use the branching process approach to obtain scaling forms for the cluster size distribution and the largest cluster size as functions of the number of edges $L$ and vertices $N$. We find that the process of forming a spanning cluster is qualitatively different between the cases of $γ>3$ and $2<γ<3$. While for the former, a spanning cluster forms abruptly at a critical number of edges $L_c$, generating a single peak in the mean cluster size $<s>$ as a function of $L$, for the latter, however, the formation of a spanning cluster occurs in a broad range of $L$, generating double peaks in $<s>$. | |
| dc.description | revised version, 4 pages, 6 figures, 1 table | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0312336 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0312336 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/22923 | |
| dc.subject | Statistical Mechanics | |
| dc.title | On the evolution of scale-free graphs | |
| dc.type | text |