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

Content Provider	Springer Nature Link
Author	Zhang, Z. Z. Zhou, S. G. Zou, T.
Copyright Year	2007
Abstract	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: scale-free degree distribution with exponent γ=2+ln 2/(ln q), null clustering coefficient, power-law behavior of grid coefficient, exponential growth of average path length (non-small-world), fractal scaling with dimension dB=ln (2q)/(ln 2), and disassortativity. 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, including its degree distribution, fractal architecture, clustering coefficient, 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 find that the self-similar property of HLs and SWHLs significantly increases the robustness of such networks against targeted damage on hubs, as compared to the very vulnerable non fractal BA networks, and that HLs have poorer synchronizability than their counterparts SWHLs and BA networks. 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.
Starting Page	259
Ending Page	271
Page Count	13
File Format	PDF
ISSN	14346028
Journal	The European Physical Journal B
Volume Number	56
Issue Number	3
e-ISSN	14346036
Language	English
Publisher	EDP Sciences
Publisher Date	2007-04-27
Publisher Place	Les Ulis
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Condensed Matter Physics Complexity Fluids Solid State Physics and Spectroscopy Superconductivity, Superfluidity, Quantum Fluids
Content Type	Text
Resource Type	Article
Subject	Electronic, Optical and Magnetic Materials Condensed Matter Physics

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