Random geometric graph

Known as: RGG, Random geometric graphs 
In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly… (More)
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Geometric graph theoryGraph theoryGraphCrunchHyperbolic geometric graph
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Papers overview

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Highly Cited
2015
Highly Cited
2015
Connectivity of soft random geometric graphs
Consider a graph on n uniform random points in the unit square, each pair being connected by an edge with probability p if the… (More)
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2015
2015
Firefighting on a random geometric graph
Let Gλ be the graph whose vertices are points of a planar Poisson process of density λ, with vertices adjacent if they are within… (More)
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2009
2009
The cover time of random geometric graphs
We study the cover time of random geometric graphs. Let I(d) = [0, 1]d denote the unit torus in d dimensions. Let D(x, r) denote… (More)
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2008
2008
Two-point concentration in random geometric graphs
A random geometric graph Gn is constructed by taking vertices X1, . . . , Xn ∈ R at random (i.i.d. according to some probability… (More)
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2006
2006
Random Geometric Graph Diameter in the Unit Ball
The unit ball random geometric graph $G=G^d_p(\lambda,n)$ has as its vertices n points distributed independently and uniformly in… (More)
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Highly Cited
2005
Highly Cited
2005
The bin-covering technique for thresholding random geometric graph properties
We study the emerging phenomenon of ad hoc, sensor-based communication networks. The communication is modeled by the geometric… (More)
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Highly Cited
2004
Highly Cited
2004
Sharp thresholds For monotone properties in random geometric graphs
Random geometric graphs result from taking n uniformly distributed points in the unit cube, [0,1]d, and connecting two points if… (More)
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2004
2004
The Spectrum of a Random Geometric Graph Is Concentrated
Consider n points distributed uniformly in [0, 1] d. Form a graph by connecting two points if their mutual distance is no greater… (More)
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2001
2001
Approximating Layout Problems on Random Geometric Graphs
In this paper, we study the approximability of several layout problems on a family of random geometric graphs. Vertices of random… (More)
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1983
1983
Hamilton cycles in random geometric graphs
We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first… (More)
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