2, edited and with a preface by Sinai (Translated from the Russian) ( Ergodic Theory with Applications to Dynamical Systems and Statistical Mechanics, Encyclopedia of Mathematical Sciences Vol. , Google Scholar Crossrefĭeterministic scale-free networks,” Physica A 299(3), 559– 564 (2001). , Google Scholar ScitationĮigenvalues and expanders,” Combinatorica 6(2), 83– 96 (1986). , Google Scholar Crossref, ISIĮigenvalues of normalized Laplacian matrices of fractal trees and dendrimers: Analytical results and applications,” J. Marvel Universe looks almost like a real social network,” preprint arXiv cond-mat/0202174 (2002). As a result of this estimation, when the bipartite base graph is complete, we give a sharp condition to ensure that our networks are well-connected with rapid mixing property. Through an elaborate analysis of our network, we can estimate its Cheeger constant, which controls the spectral gap by Cheeger inequality. It is known that a large spectral gap in terms of normalized Laplacian is usually associated with small mixing time, which makes facilitated synchronization and rapid convergence possible.
When embedding our growing network into the plane, we find its image is a graph-directed self-affine fractal, whose Hausdorff dimension is related to the power law exponent of cumulative degree distribution. To simplify our model, we suppose the base graphs are bipartite graphs and the subshift has the special form.
SUBSHIFT OF FINITE TYPE SERIES
In this paper, given a time series generated by a certain dynamical system, we construct a new class of scale-free networks with fractal structure based on the subshift of finite type and base graphs.
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