On the evolution of scale-free graphs

dc.creatorLee, D. -S.
dc.creatorGoh, K. -I.
dc.creatorKahng, B.
dc.creatorKim, D.
dc.date2003-12-13
dc.date2003-12-23
dc.date.accessioned2026-07-07T02:55:23Z
dc.date.available2026-07-07T02:55:23Z
dc.descriptionWe 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.descriptionrevised version, 4 pages, 6 figures, 1 table
dc.identifierhttps://arxiv.org/abs/cond-mat/0312336
dc.identifierhttp://arxiv.org/abs/cond-mat/0312336
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/22923
dc.subjectStatistical Mechanics
dc.titleOn the evolution of scale-free graphs
dc.typetext

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