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

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...

methods do themselves converge to an optimum, though. Rapidly exploring random graph (RRG) and RRT*, a variant of RRT that converges towards an optimal solution...

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

related to invariants of matroids, topological spaces, and matrices. In random graphs, a frequently occurring phenomenon is the incidence of a giant component...

A random r-regular graph is a graph selected from G n , r {\displaystyle {\mathcal {G}}_{n,r}} , which denotes the probability space of all r-regular...

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

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...

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...

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

Maximum-entropy random graph models are random graph models used to study complex networks subject to the principle of maximum entropy under a set of structural...

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

spanning tree, a model for a random tree. See also random walk for more general treatment of this topic. Assume G is some graph and γ {\displaystyle \gamma...

Random graph theory of gelation is a mathematical theory for sol–gel processes. The theory is a collection of results that generalise the Flory–Stockmayer...

network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often...

areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree...

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...

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...

the resulting graph may have parallel edges, but contains no self loops. Karger's basic algorithm: begin i = 1 repeat repeat Take a random edge (u,v) ∈...

research is combinatorics, particularly graph theory. His chief interests are in extremal graph theory and random graph theory. In 1996 he resigned his university...

since then. In a slightly different mathematical model for obtaining a random graph, a site is "occupied" with probability p or "empty" (in which case its...

In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian...

statistical mechanics, probability theory, graph theory, etc. the random cluster model is a random graph that generalizes and unifies the Ising model...

The Strange Logic of Random Graphs is a book on zero-one laws for random graphs. It was written by Joel Spencer and published in 2001 by Springer-Verlag...

offshoot of graph theory with Paul Erdős and Alfréd Rényi's eight famous papers on random graphs. For social networks the exponential random graph model or...

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...

component arises. The structure of a gel network can be conceptualised as a random graph. This analogy is exploited to calculate the gel point and gel fraction...

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...

mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...