Results 11 to 20 of about 210 (139)
Physical Review E, 2023 There is a well-known relationship between the binary Pascal's triangle and Sierpinski triangle in which the latter obtained from the former by successive modulo 2 additions on one of its corners. Inspired by that, we define a binary Apollonian network and obtain two structures featuring a kind of dendritic growth.
Eduardo M. K. Souza +1 more
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Long Paths in Random Apollonian Networks [PDF]
Internet Mathematics, 2015 We consider the length L(n) of the longest path in a randomly generated Apollonian Network (ApN) . We show that with high probability for any constant c < 2/3.
Colin Cooper, Alan M. Frieze
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On Certain Properties of Random Apollonian Networks [PDF]
, 2012 In this work we analyze fundamental properties of Random Apollonian Networks [34,35], a popular random graph model which generates planar graphs with power law properties. Specifically, we analyze (a) the degree distribution, (b) the k largest degrees, (c) the k largest eigenvalues and (d) the diameter, where k is a constant.
Alan M. Frieze +1 more
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Degrees and distances in random and evolving apollonian networks [PDF]
Advances in Applied Probability, 2016 Abstract In this paper we study random Apollonian networks (RANs) and evolving Apollonian networks (EANs), in d dimensions for any d≥2, i.e. dynamically evolving random d-dimensional simplices, looked at as graphs inside an initial d-dimensional simplex.
Kolossváry, István +2 more
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Magnetic models on Apollonian networks [PDF]
Physical Review E, 2005 Thermodynamic and magnetic properties of Ising models defined on the triangular Apollonian network are investigated. This and other similar networks are inspired by the problem of covering an Euclidian domain with circles of maximal radii. Maps for the thermodynamic functions in two subsequent generations of the construction of the network are obtained
Andrade, Roberto F. S. +1 more
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ENERGY LANDSCAPES, SCALE-FREE NETWORKS AND APOLLONIAN PACKINGS [PDF]
Complexity, Metastability and Nonextensivity, 2005 10 pages, 8 ...
Doye, J, Massen, C
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Random Apollonian networks with tailored clustering coefficient
Physical Review E6 pages, 7 ...
Eduardo M. K. Souza +1 more
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Phase Transitions in Equilibrium and Non-Equilibrium Models on Some Topologies
Entropy, 2016 On some regular and non-regular topologies, we studied the critical properties of models that present up-down symmetry, like the equilibrium Ising model and the nonequilibrium majority vote model. These are investigated on networks, like Apollonian (AN),
Francisco W. De Sousa Lima
doaj +2 more sources
A Survey of Maximal k-Degenerate Graphs and k-Trees
Theory and Applications of GraphsThis article surveys results on maximal $k$-degenerate graphs, $k$-trees, and related classes including simple $k$-trees, $k$-paths, maximal outerplanar graphs, and Apollonian networks.
Allan Bickle
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Modified diffusive epidemic process on Apollonian networks. [PDF]
J Biol Phys, 2023 We present an analysis of an epidemic spreading process on an Apollonian network that can describe an epidemic spreading in a non-sedentary population. We studied the modified diffusive epidemic process using the Monte Carlo method by computational analysis.
Alencar D +5 more
europepmc +3 more sources