Results 21 to 30 of about 2,487,806 (297)
Random Walk Graph Auto-Encoders With Ensemble Networks in Graph Embedding
IEEE Access, 2023 Recently graph auto-encoders have received increasingly widespread attention as one of the important models in the field of deep learning. Existing graph auto-encoder models only use graph convolutional neural networks (GCNs) as encoders to learn the ...
Chengxin Xie +3 more
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Logconcave random graphs [PDF]
Proceedings of the fortieth annual ACM symposium on Theory of computing, 2008 We propose the following model of a random graph on $n$ vertices. Let $F$ be a distribution in $R_+^{n(n-1)/2}$ with a coordinate for every pair $ij$ with $1 \le i,j \le n$. Then $G_{F,p}$ is the distribution on graphs with $n$ vertices obtained by picking a random point $X$ from $F$ and defining a graph on $n$ vertices whose edges are pairs $ij$ for ...
Alan M. Frieze +2 more
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Physical Review E, 2002 We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size of the largest cluster. We derive an analytical expression for the cluster coefficient which shows that the graphs
Dall, J., Christensen, Michael
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Connectivity of Random Geometric Hypergraphs
Entropy, 2023 We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie within a certain radius.
Henry-Louis de Kergorlay +1 more
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Random Graph Isomorphism [PDF]
SIAM Journal on Computing, 1980 Summary: A straightforward linear time canonical labeling algorithm is shown to apply to almost all graphs (i.e. all but \(O(2^{\binom n2})\) of the \(2^{\binom n2})\) graphs on \(n\) vertices). Hence, for almost all graphs \(X\), and graph \(Y\) can be easily tested for isomorphism to \(X\) by an extremly naive linear time algorithm.
László Babai +2 more
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On the Hyperbolicity of Random Graphs [PDF]
The Electronic Journal of Combinatorics, 2014 Let $G=(V,E)$ be a connected graph with the usual (graph) distance metric $d:V \times V \to \mathbb{N} \cup \{0 \}$. Introduced by Gromov, $G$ is $\delta$-hyperbolic if for every four vertices $u,v,x,y \in V$, the two largest values of the three sums $d(u,v)+d(x,y)$, $d(u,x)+d(v,y)$, $d(u,y)+d(v,x)$ differ by at most $2\delta$.
Dieter Mitsche, Pawel Pralat
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The Electronic Journal of Combinatorics, 2023 Let $N=\binom{n}{2}$ and $s\geq 2$. Let $e_{i,j},\,i=1,2,\ldots,N,\,j=1,2,\ldots,s$ be $s$ independent permutations of the edges $E(K_n)$ of the complete graph $K_n$. A MultiTree is a set $I\subseteq [N]$ such that the edge sets $E_{I,j}$ induce spanning trees for $j=1,2,\ldots,s$.
Alan M. Frieze, Wesley Pegden
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Data Collection Based on Opportunistic Node Connections in Wireless Sensor Networks
Sensors, 2018 The working⁻sleeping cycle strategy used for sensor nodes with limited power supply in wireless sensor networks can effectively save their energy, but also causes opportunistic node connections due to the intermittent communication mode, which can ...
Guisong Yang, Zhiwei Peng, Xingyu He
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The Electronic Journal of Combinatorics, 2009 We study a random even subgraph of a finite graph $G$ with a general edge-weight $p\in(0,1)$. We demonstrate how it may be obtained from a certain random-cluster measure on $G$, and we propose a sampling algorithm based on coupling from the past. A random even subgraph of a planar lattice undergoes a phase transition at the parameter-value ${1\over2 ...
Geoffrey R. Grimmett, Svante Janson
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The Electronic Journal of Combinatorics, 2009 We introduce a pair of natural, equivalent models for random threshold graphs and use these models to deduce a variety of properties of random threshold graphs. Specifically, a random threshold graph $G$ is generated by choosing $n$ IID values $x_1,\ldots,x_n$ uniformly in $[0,1]$; distinct vertices $i,j$ of $G$ are adjacent exactly when $x_i + x_j \ge
Elizabeth Perez Reilly +1 more
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