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Random regular graph

About: Random regular graph is a research topic. Over the lifetime, 2850 publications have been published within this topic receiving 97633 citations.


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Book
01 Sep 1985

7,736 citations

Book
13 Mar 2000

2,591 citations

Journal ArticleDOI
TL;DR: It is shown that if Σ i(i - 2)λi > 0, then such graphs almost surely have a giant component, while if λ0, λ1… which sum to 1, then almost surely all components in such graphs are small.
Abstract: Given a sequence of nonnegative real numbers λ0, λ1… which sum to 1, we consider random graphs having approximately λi n vertices of degree i. Essentially, we show that if Σ i(i - 2)λi > 0, then such graphs almost surely have a giant component, while if Σ i(i -2)λ. < 0, then almost surely all components in such graphs are small. We can apply these results to Gn,p,Gn.M, and other well-known models of random graphs. There are also applications related to the chromatic number of sparse random graphs. © 1995 Wiley Periodicals, Inc.

2,494 citations

01 Jan 2001
TL;DR: Estimates on the important parameters of access time, commute time, cover time and mixing time are discussed and recent algorithmic applications of random walks are sketched, in particular to the problem of sampling.
Abstract: Various aspects of the theory of random walks on graphs are surveyed In particular, estimates on the important parameters of access time, commute time, cover time and mixing time are discussed Connections with the eigenvalues of graphs and with electrical networks, and the use of these connections in the study of random walks is described We also sketch recent algorithmic applications of random walks, in particular to the problem of sampling

1,564 citations

Journal ArticleDOI
TL;DR: An analytical expression for the cluster coefficient is derived, which shows that the graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality are distinctly different from standard random graphs, even for infinite dimensionality.
Abstract: We analyze graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size of the largest cluster. We derive an analytical expression for the cluster coefficient, which shows that the graphs are distinctly different from standard random graphs, even for infinite dimensionality. Insights relevant for graph bipartitioning are included.

1,271 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202226
202111
20209
20197
201823