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

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

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

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...

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...

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...

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

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

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...

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...

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

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...

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

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

Exponential family random graph models (ERGMs) are a set of statistical models used to study the structure and patterns within networks, such as those...

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...

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...

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...

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

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...

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

phs (L:B) Percolation threshold / phs Random geometric graph Random regular graph Watts and Strogatz model Random matrix Circular ensemble Gaussian matrix...

networks were identified as a class of random graphs by Duncan Watts and Steven Strogatz in 1998. They noted that graphs could be classified according to two...

Periodic graphs are closely related to tessellations of space (or honeycombs) and the geometry of their symmetry groups, hence to geometric group theory...

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...