Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices

Simple item page
dc.creatorZhang, Zhongzhi
dc.creatorZhou, Shuigeng
dc.creatorZou, Tao
dc.date2006-12-16
dc.date.accessioned2026-07-07T07:59:21Z
dc.date.available2026-07-07T07:59:21Z
dc.descriptionIn this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter $q$. Our results show that scale-free networks are not always small-world, and support the conjecture that self-similar scale-free networks are not assortative. Secondly, we define a deterministic family of graphs called small-world hierarchical lattices (SWHLs). Our construction preserves the structure of hierarchical lattices, while the small-world phenomenon arises. Finally, the dynamical processes of intentional attacks and collective synchronization are studied and the comparisons between HLs and Barab{ási}-Albert (BA) networks as well as SWHLs are shown. We show that degree distribution of scale-free networks does not suffice to characterize their synchronizability, and that networks with smaller average path length are not always easier to synchronize.
dc.description26 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0612427
dc.identifierhttp://arxiv.org/abs/cond-mat/0612427
dc.identifierEur. Phys. J. B 56, 259-271 (2007)
dc.identifierdoi:10.1140/epjb/e2007-00107-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128334
dc.subjectStatistical Mechanics
dc.titleSelf-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices
dc.typetext

Files

Collections

arXiv