Tail bounds for the height and width of a random tree with a given degree sequence

Random graphs with a given degree sequence

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have graph limits in the sense of Lovász and Szegedy with identifiable limits. This allows simple determination of other features such as the number of triangles. ...

The cores of random hypergraphs with a given degree sequence

$\beta$ models for random hypergraphs with a given degree sequence

Abstract: We introduce the beta model for random hypergraphs in order to represent the occurrence of multi-way interactions among agents in a social network. This model builds upon and generalizes the well-studied beta model for random graphs, which instead only considers pairwise interactions. We provide two algorithms for fitting the model parameters, IPS (iterative proportional scaling) and ...

Β Models for Random Hypergraphs with a given Degree Sequence

Abstract: We introduce the beta model for random hypergraphs in order to represent the occurrence of multi-way interactions among agents in a social network. This model builds upon and generalizes the well-studied beta model for random graphs, which instead only considers pairwise interactions. We provide two algorithms for fitting the model parameters, IPS (iterative proportional scaling) and ...

Cover time of a random graph with given degree sequence

In this paper we establish the cover time of a random graph G(d) chosen uniformly at random from the set of graphs with vertex set [n] and degree sequence d. We show that under certain restrictions on d, the cover time of G(d) is whp asymptotic to d−1 d−2 θ dn log n. Here θ is the average degree and d is the effective minimum degree.