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...any times, and the subset among all possible subsets that yields the least random (furthest from uniform distribution) selection of right vertices is <math>\ ...obtained by choosing a random node in <math>A</math> and then following a random [[graph theory|edge]] to get a node x on the right side is <math>\epsilon</ ...

...y be formed by assigning [[Independence (probability theory)|independent]] random weights from some distribution to the edges of an [[undirected graph]], and [[File:Random minimum spanning tree.svg|thumb|380px|Random minimum spanning tree on the same graph but with randomized weights.]] ...

{{Short description|Large connected component of a random graph}} ...rt graph.svg|thumb|upright=1.35|An [[Erdős–Rényi model|Erdős–Rényi–Gilbert random graph]] with 1000 vertices at the critical edge probability <math>p=1/(n-1) ...

{{short description|Graph generated by a random process}} {{for|the countably-infinite random graph|Rado graph}} ...

...tions to discrete mathematics and theory of computing, particularly random graphs and networks, Ramsey theory, logic, and randomized algorithms".<ref>[http:/ * ''[[The Strange Logic of Random Graphs|The strange logic of random graphs]]'', Berlin: Springer-Verlag, 2001. ...

...st3 = M. A. | doi = 10.1038/nature03204 | title = Evolutionary dynamics on graphs | journal = Nature | volume = 433 | issue = 7023 | pages = 312–316 | year = One property studied on graphs with two types of individuals is the ''fixation probability'', which is def ...

...hm|sum–product algorithm]]. One of the important success stories of factor graphs and the sum–product algorithm is the [[code|decoding]] of capacity-approach ...ph where all factors are constraints. The max-product algorithm for factor graphs can be viewed as a generalization of the [[Local_consistency#Arc_consistenc ...

...s''', after the mathematical objects called [[Graph (discrete mathematics)|graphs]] studied in [[graph theory]]. ...[directed graph]], which might be [[Cycle graph|cyclic]]. When stored in [[Random access memory|RAM]], objects occupy different segments of the memory with t ...

The problem of finding Hamiltonian paths in highly symmetric graphs is quite old. As [[Donald Knuth]] describes it in volume 4 of ''[[The Art o ...triangle.<ref>{{citation |first=Gordon |last=Royle |title=Cubic Symmetric Graphs (The Foster Census) |date= |work= |url=http://www.cs.uwa.edu.au/~gordon/rem ...

==Examples and types of graphs== * [[Interval graph#Improper interval graphs|Interval graph, proper]] ...

| title = Universal graphs and universal functions | title = Universal graphs ...

...ch an optimization problem is called an '''extremal graph''', and extremal graphs are important objects of study in extremal graph theory. ...denoted <math>\chi(G)</math>. Determining the chromatic number of specific graphs is a fundamental question in extremal graph theory, because many problems i ...

...be a '''pseudorandom graph''' if it obeys certain properties that [[random graphs]] obey [[with high probability]]. There is no concrete definition of graph ...5 |pages=199–262 |chapter-url=https://people.math.ethz.ch/~sudakovb/pseudo-random-survey.pdf|doi=10.1007/978-3-540-32439-3_10 |isbn=978-3-540-32377-8 |series ...

...edges, and a {{nowrap|2-regular}} graph consists of a [[disjoint union of graphs|disjoint union]] of [[cycle (graph theory)|cycle]]s and infinite chains. ...c graph]], respectively. Similarly, it is possible to denote ''k''-regular graphs with <math>k=5,6,7,8,\ldots</math> as quintic, sextic, septic, octic, ''et& ...

...ays close to the expected number of edges between them in a [[random graph|random]] <math>d</math>-[[regular graph]], namely <math>\frac dn|S||T|</math>. == ''d''-Regular Expander Graphs == ...

| title = Spectra of random graphs with given expected degrees Note that in the case of undirected graphs, an edge that starts and ends in the same node increases the corresponding ...

...formed from a [[Poisson point process]], making them a simple example of a random structure. * Unit disk graphs are the graphs formed from a collection of points in the Euclidean plane, with a vertex fo ...

...on the space of [[cumulative distribution function]]s of one-dimensional [[random variable]]s. It is a special case of the [[Lévy–Prokhorov metric]], and is Intuitively, if between the graphs of ''F'' and ''G'' one inscribes squares with sides parallel to the coordin ...

...inite family of symmetric [[conference matrix|conference matrices]]. Paley graphs allow [[graph-theoretic]] tools to be applied to the [[number theory]] of q Paley graphs are named after [[Raymond Paley]]. They are closely related to the [[Paley ...

...]] in the [[1. Liga Classic]]. He has a side interest in random geometric graphs. ...