Displaying similar documents to “Asymptotic spectral analysis of generalized Erdős-Rényi random graphs”

Matrix and discrepancy view of generalized random and quasirandom graphs

Marianna Bolla, Ahmed Elbanna (2016)

Special Matrices

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We will discuss how graph based matrices are capable to find classification of the graph vertices with small within- and between-cluster discrepancies. The structural eigenvalues together with the corresponding spectral subspaces of the normalized modularity matrix are used to find a block-structure in the graph. The notions are extended to rectangular arrays of nonnegative entries and to directed graphs. We also investigate relations between spectral properties, multiway discrepancies,...

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...

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.

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...

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.