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Taylor’s power law for the
Modern Stochastics: Theory and Applications, 2019 Taylor’s power law states that the variance function decays as a power law. It is observed for population densities of species in ecology. For random networks another power law, that is, the power law degree distribution is widely studied.
István Fazekas +2 more
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Random rectangular graphs [PDF]
Physical Review E, 2015 A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides ...
Estrada, Ernesto, Sheerin, Matthew
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The number of planar graphs and properties of random planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We show an asymptotic estimate for the number of labelled planar graphs on $n$ vertices. We also find limit laws for the number of edges, the number of connected components, and other parameters in random planar graphs.
Omer Gimenez, Marc Noy
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A Continuous-Time Network Evolution Model Describing 2- and 3-Interactions
Mathematics, 2021 A continuous-time network evolution model is considered. The evolution of the network is based on 2- and 3-interactions. 2-interactions are described by edges, and 3-interactions are described by triangles.
István Fazekas, Attila Barta
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Universality of Random Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2012 We prove that asymptotically (as $n\to\infty$) almost all graphs with $n$ vertices and $C_dn^{2-\frac{1}{2d}} \log^{\frac{1}{d}} n$ edges are universal with respect to the family of all graphs with maximum degree bounded by $d$. Moreover, we provide an efficient deterministic embedding algorithm for finding copies of bounded degree graphs in graphs ...
Domingos Dellamonica Jr. +3 more
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On hamiltonicity of uniform random intersection graphs
Lietuvos Matematikos Rinkinys, 2010 We give a sufficient condition for the hamiltonicity of the uniform random intersection graph G{n,m,d}. It is a graph on n vertices, where each vertex is assigned d keys drawn independently at random from a given set of m keys, and where any two vertices
Mindaugas Bloznelis +1 more
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Asymptotic Behavior of the Edge Metric Dimension of the Random Graph
Discussiones Mathematicae Graph Theory, 2021 Given a simple connected graph G(V,E), the edge metric dimension, denoted edim(G), is the least size of a set S ⊆ V that distinguishes every pair of edges of G, in the sense that the edges have pairwise different tuples of distances to the vertices of S.
Zubrilina Nina
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Combinatorica, 1988 We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this class.
Chung, F. R. K. +2 more
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Random Graphs with Clustering [PDF]
Physical Review Letters, 2009 We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be neighbors of one another.
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Random matrices and random graphs
ESAIM: Proceedings and Surveys, 2023 We collect recent results on random matrices and random graphs. The topics covered are: fluctuations of the empirical measure of random matrices, finite-size effects of algorithms involving random matrices, characteristic polynomial of sparse matrices and Voronoi tesselations of split trees.
Capitaine Mireille +4 more
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