In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing...

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability...

probability). A HGG generalizes a random geometric graph (RGG) whose embedding space is Euclidean. Mathematically, a HGG is a graph G ( V , E ) {\displaystyle...

network is a lattice or a random geometric graph (see figure in the right), where nodes are distributed uniformly at random over a two-dimensional plane;...

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...

and geometric group theory. The structure and symmetry of Cayley graphs make them particularly good candidates for constructing expander graphs. Let...

graphs of infinite random point sets, the finite site percolation threshold gives the fraction of points needed to support connectivity: if a random subset...

software originally developed by NRL. The traditional model is the random geometric graph. Early work included simulating ad hoc mobile networks on sparse...

field of graph theory, the Erdős–Rényi model refers to one of two closely related models for generating random graphs or the evolution of a random network...

polytope, unit disk graphs, and visibility graphs. Topics in this area include: Graph drawing Polyhedral graphs Random geometric graphs Voronoi diagrams...

geometric group theory is to consider finitely generated groups themselves as geometric objects. This is usually done by studying the Cayley graphs of...

In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one...

In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander...

S2CID 122784453. Seidel R. Backwards Analysis of Randomized Geometric Algorithms. Karger, David R. (1999). "Random Sampling in Cut, Flow, and Network Design...

showing that every monotone graph property has a sharp threshold in geometric random graphs; and showing that in a packet switch, output queuing (the gold...

two types of percolation theory as well as the study of random graphs and random geometric graphs. Continuum percolation arose from an early mathematical...

distances bounded. A random walk on a graph is a very special case of a Markov chain. Unlike a general Markov chain, random walk on a graph enjoys a property...

In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors...

objects of exchangeable random graph models. Graphons are tied to dense graphs by the following pair of observations: the random graph models defined by graphons...

RGG may refer to: Random geometric graph, a concept in mathematical graph theory Responsible Government Group (2009), a centre-right caucus in the City...

of a directed graph, in which case it can be used to analyze how quickly random walks in the graph converge. The conductance of a graph is closely related...

transmission, the Erdős–Rényi–Gilbert model for random graphs, the Gilbert disk model of random geometric graphs, the Gilbert–Shannon–Reeds model of card shuffling...

spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are...

algorithms for creating a knowledge graph embedding follow the same approach. First, the embedding vectors are initialized to random values. Then, they are iteratively...

transformation which converts random graphs to their edge-dual graphs (or line graphs) produces an ensemble of graphs with nearly the same degree distribution...

In network science, a biased random walk on a graph is a time path process in which an evolving variable jumps from its current state to one of various...

be built on message passing over suitably defined graphs. In the more general subject of "geometric deep learning", certain existing neural network architectures...

computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it...