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Stochastic Processes and their Applications, 1974 AbstractIn this paper the following Markov chains are considered: the state space is the set of vertices of a connected graph, and for each vertex the transition is always to an adjacent vertex, such that each of the adjacent vertices has the same probability.
F. Göbel, A. A. Jagers
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Directed network Laplacians and random graph models [PDF]
Royal Society Open Science, 2021 We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph model. We focus on
Xue Gong +2 more
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Subgraphs of Random Graphs [PDF]
Transactions of the American Mathematical Society, 1985 Let Δ ⊆ [ ω ] 2 \Delta \subseteq {[\omega ]^2} be an undirected graph on ω \omega , and let u ∈ [ 0 , 1 ] u \in [0,\,1] . Following P. Erdös and A.
D. H. Fremlin, Michel Talagrand
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Discrete Applied Mathematics, 1994 AbstractWe do a probabilistic analysis of the problem of distributing a single piece of information to the vertices of a graph G. Assuming that the input graph G is Gn,p, we prove an O(ln n/n) upper bound on the edge density needed so that with high probability the information can be broadcast in ⌈log2 n⌉ rounds.
Alan Frieze, Michael Molloy
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Degree distribution in random planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We prove that for each $k \geq 0$, the probability that a root vertex in a random planar graph has degree $k$ tends to a computable constant $d_k$, and moreover that $\sum_k d_k =1$. The proof uses the tools developed by Gimènez and Noy in their solution
Michael Drmota, Omer Gimenez, Marc Noy
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The Spectral Distribution of Random Mixed Graphs
Axioms, 2022 In this work, we propose a random mixed graph model Gn(p(n),q(n)) that incorporates both the classical Erdős-Rényi’s random graph model and the random oriented graph model.
Yue Guan +7 more
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The Random Plots Graph Generation Model for Studying Systems with Unknown Connection Structures
Entropy, 2022 We consider the problem of modeling complex systems where little or nothing is known about the structure of the connections between the elements. In particular, when such systems are to be modeled by graphs, it is unclear what vertex degree distributions
Evgeny Ivanko, Mikhail Chernoskutov
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Random walks on the random graph [PDF]
The Annals of Probability, 2018 We study random walks on the giant component of the Erdős–Rényi random graph G(n,p) where p=λ/n for λ>1 fixed. The mixing time from a worst starting point was shown by Fountoulakis and Reed, and independently by Benjamini, Kozma and Wormald, to have order log2n.
Berestycki, Nathanaël +3 more
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Limit Theorem for Spectra of Laplace Matrix of Random Graphs
Mathematics, 2023 We consider the limit of the empirical spectral distribution of Laplace matrices of generalized random graphs. Applying the Stieltjes transform method, we prove under general conditions that the limit spectral distribution of Laplace matrices converges ...
Alexander N. Tikhomirov
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