Mathematics Random Sparse Graphs with a Given Degree Sequence NEW YORK UNIVERSITY Sourav ChatterjeeSrinivasa R. S. Varadhan MehrdadBehzadLet be the set of graphs with vertices, and the degree sequence equal to In addition, for we define the set of graphs with an almost given degree sequence as...
random graph with given degreesWe consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model and then, by a conditioning...
power law graphsWe consider a family of random graphs with a given expected degree sequence. Each edge is chosen independently with probability proportional to the product of the expected degrees of its endpoints. We examine the distribution of the sizes/volumes of the connected components which ...
The size of the largest strongly connected component of a random digraph with a given degree sequence. Combin. Probab. ... C Cooper,A Frieze - 《Combinatorics Probability & Computing》 被引量: 133发表: 2004年 Sparse random graphs with a given degree sequence Let ${\\\bold d}= (d\\\sb...
Joseph, A. (2014). The component sizes of a critical random graph with given degree sequence. Ann. Appl. Probab., 24(6):2560-2594.A. Joseph et al., The component sizes of a critical random graph with given degree sequence, The Annals of Applied Probability 24 (2014), no. 6, 2560...
1 Introduction Various papers (see e.g., [4, 7, 13, 18, 20]) study properties of random graphs with a given degree sequence. Among such properties as connectivity, cluster size and diameter, the graph distance between two uniformly chosen nodes is an important one. For two connected ...
We propose a random graph model which is a special case of sparserandom graphs with given degree sequences which satisfy a power law. This model involves only a small number of paramo eters, called logsize and log-log growth rate. These parameters capture some universal characteristics of ...
The most popular family of random graph null models, called configuration models, are defined as uniform distributions over a space of graphs with a fixed degree sequence. Commonly, properties of an empirical network are compared to properties of an ensemble of graphs from a configuration model in...
1.3 Previous Work Strictly speaking our model is a special case of random graphs with a given degree sequence for which there is a large literature. For example, Wormald [17] studied the connectivity of graphs whose degrees are in an interval [r, R], where r ≥ 3. Luczak [13] ...
We study in particular the random graph defined as the uniform distribution on graphs with a given degree sequence. We characterise degree sequences that define contiguous random graph sequences, and in particular contiguous to an Erd艖s-R茅nyi random graph. The method allows to extend a result...