منابع مشابه
High dimensional Apollonian networks
We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension. PACS numbers: 89.75.Hc, 89.75.Da, 89.20.Hh High dimensional Apollonian networks 2
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We present and study in this paper a simple algorithm that produces so called growing Parallel Random Apollonian Networks (P-RAN) in any dimension d. Analytical derivations show that these networks still exhibit small-word and scalefree characteristics. To characterize further the structure of P-RAN, we introduce new parameters that we refer to as the parallel degree and the parallel coefficien...
متن کاملApollonian Circle Packings
Figure 1: An Apollonian Circle Packing Apollonius’s Theorem states that given three mutually tangent circles, there are exactly two circles which are tangent to all three. Apollonian circle packings are produced by repeating the construction of mutually tangent circles to fill all remaining spaces. A remarkable consequence of Descartes’ Theorem is if the initial four tangent circles have integr...
متن کاملIntegral Apollonian Packings
We review the construction of integral Apollonian circle packings. There are a number of Diophantine problems that arise in the context of such packings. We discuss some of them and describe some recent advances. 1. AN INTEGRAL PACKING. The quarter, nickel, and dime in Figure 1 are placed so that they are mutually tangent. This configuration is unique up to rigid motions. As far as I can tell t...
متن کاملApollonian Circle Packings
Circle packings are a particularly elegant and simple way to construct quite complicated and elaborate sets in the plane. One systematically constructs a countable family of tangent circles whose radii tend to zero. Although there are many problems in understanding all of the individual values of their radii, there is a particularly simple asymptotic formula for the radii of the circles, origin...
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ژورنال
عنوان ژورنال: EPL (Europhysics Letters)
سال: 2020
ISSN: 1286-4854
DOI: 10.1209/0295-5075/130/38001