2006/12/16 by Zhongzhi Zhang, Z.-Z. Zhang, Shuigeng Zhou +3
Computer Science · Physics and Astronomy · #Average path length #Complex Network Analysis Techniques #Complex network #Conjecture #Degree (music) #Degree distribution #Fractal #Grid #Neural Networks Stability and Synchronization #Opinion Dynamics and Social Influence #Robustness (evolution) #Scaling #Topology (electrical circuits) #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2007-00107-6
published as Eur. Phys. J. B 56, 259-271 (2007) · 26 pages, 8 figures
arxiv created 2006/12/16 · openalex publication_date 2007/04/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In 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 Barabási-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.