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A random geometric graph (RGG) is an undirected geometric graph with nodes randomly sampled from the uniform distribution of the underlying space [0,1)d. [3] Two vertices p, q ∈ V are connected if, and only if, their distance is less than a previously specified parameter r ∈ (0,1), excluding any loops. Thus, the parameters r and n fully ...
Network science. In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. [1][2] The theory of random graphs lies at the intersection between graph theory and probability theory.
The geometric distribution is the discrete probability distribution that describes when the first success in an infinite sequence of independent and identically distributed Bernoulli trials occurs. Its probability mass function depends on its parameterization and support.
Network science. A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are spatial elements associated with geometric objects, i.e., the nodes are located in a space equipped with a certain metric. [1][2] The simplest mathematical realization of spatial network is a lattice or a random geometric graph (see ...
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are ...
Stochastic geometry. A possible stochastic geometry model (Boolean model) for wireless network coverage and connectivity constructed from randomly sized disks placed at random locations. In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the subject lies the study of random point patterns.
A geometric graph is a graph in which the vertices or edges are associated with geometric objects. Examples include Euclidean graphs, the 1-skeleton of a polyhedron or polytope, unit disk graphs, and visibility graphs. Topics in this area include: Graph drawing; Polyhedral graphs; Random geometric graphs; Voronoi diagrams and Delaunay ...
The Rado graph, as numbered by Ackermann (1937) and Rado (1964). In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with probability one) by choosing independently at random for each pair of its vertices whether to connect the vertices by an edge.