Results 121 to 130 of about 210 (139)
High-dimensional random Apollonian networks [PDF]
Physica A: Statistical Mechanics and Its Applications, 2006 We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network.
Zhongzhi Zhang +2 more
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On longest paths and diameter in random apollonian networks [PDF]
Random Structures and Algorithms, 2014 ABSTRACTWe consider the following iterative construction of a random planar triangulation. Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and join it to the vertices of the face.
Pu Gao, Abbas Mehrabian
exaly +3 more sources
Some of the next articles are maybe not open access.
THREE-DIMENSIONAL APOLLONIAN NETWORKS
International Journal of Modern Physics C, 2006We discuss the three-dimensional Apollonian network introduced by Andrade et al.1 for the two-dimensional case. These networks are simultaneously scale-free, small world, Euclidean, space-filling and matching graphs and have a wide range of applications going from the description of force chains in polydisperse granular packings to the geometry of ...
Soares, Danyel J. B. +3 more
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Spectral properties of the Apollonian network
Physica A: Statistical Mechanics and Its Applications, 2005Abstract A first characterization of the spectral properties of the Apollonian network is presented. Results are based on the numerically evaluated eigenvalue spectra of adjacency matrices for the first nine generations of the network. The main features refer to the presence of several gaps on the eigenvalue axis and a very large number of ...
Roberto F S Andrade +1 more
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On the Longest Paths and the Diameter in Random Apollonian Networks [PDF]
Electronic Notes in Discrete Mathematics, 2013 We consider the following iterative construction of a random planar triangulation. Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and join it to the vertices of the face.
Pu Gao +2 more
exaly +3 more sources
Heavy subtrees of Galton-Watson trees with an application to Apollonian networks [PDF]
Electronic Journal of Probability, 2019 We study heavy subtrees of conditional Galton-Watson trees. In a standard Galton-Watson tree conditional on its size being n, we order all children by their subtree sizes, from large (heavy) to small.
Luc Devroye, Cecilia Holmgren
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Two-point resistances in an Apollonian network
Physical Review E, 2017The computation of resistance between two nodes in a resistor network is a classical problem in electric theory and graph theory. Based on the Apollonian packing, Andrade et al. introduced a deterministic growing type of networks A(k) [Phys. Rev. Lett. 94, 018702 (2005)PRLTAO0031-900710.1103/PhysRevLett.94.018702].
Yingmin, Shangguan, Haiyan, Chen
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Type-II Apollonian network: More robust and more efficient Apollonian network
Chaos, Solitons and FractalsFei Ma +4 more
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Tutte polynomial of the Apollonian network
Journal of Statistical Mechanics: Theory and Experiment, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liao, Yunhua +2 more
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Finite-size effects for percolation on Apollonian networks
Physical Review E, 2008We study the percolation problem on the Apollonian network model. The Apollonian networks display many interesting properties commonly observed in real network systems, such as small-world behavior, scale-free distribution, and a hierarchical structure.
Daniel M, Auto +3 more
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