Displaying similar documents to “Finite-size scaling in percolation.”

Random even graphs.

Grimmett, Geoffrey, Janson, Svante (2009)

The Electronic Journal of Combinatorics [electronic only]

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Random procedures for dominating sets in bipartite graphs

Sarah Artmann, Jochen Harant (2010)

Discussiones Mathematicae Graph Theory

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Using multilinear functions and random procedures, new upper bounds on the domination number of a bipartite graph in terms of the cardinalities and the minimum degrees of the two colour classes are established.

A stationary random graph of no growth rate

Ádám Timár (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We present a random automorphism-invariant subgraph of a Cayley graph such that with probability 1 its exponential growth rate does not exist.

Limit theorems for the weights and the degrees in anN-interactions random graph model

István Fazekas, Bettina Porvázsnyik (2016)

Open Mathematics

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A random graph evolution based on interactions of N vertices is studied. During the evolution both the preferential attachment rule and the uniform choice of vertices are allowed. The weight of an M-clique means the number of its interactions. The asymptotic behaviour of the weight of a fixed M-clique is studied. Asymptotic theorems for the weight and the degree of a fixed vertex are also presented. Moreover, the limits of the maximal weight and the maximal degree are described. The...

TPM: Transition probability matrix - Graph structural feature based embedding

Sarmad N. Mohammed, Semra Gündüç (2023)

Kybernetika

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In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The information obtained from random walks is converted to anonymous walks to extract the topological features of nodes. In the embedding process of nodes, anonymous walks are used since they capture the topological similarities of connectivities better...

Scaling of a random walk on a supercritical contact process

F. den Hollander, R. S. dos Santos (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the...

How the result of graph clustering methods depends on the construction of the graph

Markus Maier, Ulrike von Luxburg, Matthias Hein (2013)

ESAIM: Probability and Statistics

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We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable partition of the graph. Our main question is if and how the construction of the graph (choice of the graph, choice of parameters, choice of weights) influences the outcome of the final clustering result. To this end we study the convergence of cluster quality...

Cluster continuous time random walks

Agnieszka Jurlewicz, Mark M. Meerschaert, Hans-Peter Scheffler (2011)

Studia Mathematica

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In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly...

Asymptotic spectral analysis of generalized Erdős-Rényi random graphs

Song Liang, Nobuaki Obata, Shuji Takahashi (2007)

Banach Center Publications

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Motivated by the Watts-Strogatz model for a complex network, we introduce a generalization of the Erdős-Rényi random graph. We derive a combinatorial formula for the moment sequence of its spectral distribution in the sparse limit.