Random Geometric Graphs

By Mathew D. Penrose. 2003

375 citations recorded by the source corpus.

Subfields: Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ea21791255647a9c758b9ec2ba8bf1f2269f8864

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In Computer Graphics and Computer-Aided Design

In Discrete Mathematics and Combinatorics

In Mathematical Physics

Citations in the corpus

Extremal Properties of Random Structures (2003, neutral): “ vertices with edges to v. In principle one could study such models based on random points in ddimensional space, but within such settings it is notoriously hard to do explicit calculations (see e.g. [16] for diﬀerent models of random graphs based on ddimensional random points), and the choice of d ”
Directed graphs, Hamiltonicity and doubly stochastic matrices (2004, background): “Including extensions to higher dimensions, numerous related problems are investigated in the monographs by Hall [10], Aldous [1], Barbour, Holst and Janson [2], and Penrose [16], in the four-part survey by Hüsler [15] and in their vast number of references.”
Topology and data (2009, background): “Penrose and others have developed a theory of “geometric random graphs” and have proved various results concerning the Betti numbers of complexes attached to such graphs (see [54]).”
D-ADMM: A Communication-Efficient Distributed Algorithm for Separable Optimization (2012, background): “Geometric [42] d It drops P points, corresponding to the nodes of the network, randomly in a [0, 1] square; then, it connects nodes whose (Euclidean) distance is less than d.”
Recurrence versus transience for weight-dependent random connection models (2019, background): “we summarize some of them in Table 1. Table1. Terminology of the models in the literature. Vertices Proﬁle Kernel Name and reference Poisson indicator plain Random geometric graph, Gilbert disc model [24] Poisson general plain Random connection model [18] Soft random geometric graph [23] lattice pol”
The local weak limit of the minimum spanning tree of the complete graph (2013, background): “ the large-nscaling of various other \localizable" functionals of random Euclidean MST’s ([56,57,58,68,42]. (The above references are representative, rather than exhaustive. The books of Penrose [59] and of Yukich [76] are comprehensive compendia of the known results and techniques for such pro”