Spectral graph theoretic methods have recently shown great promise for the problem of
image segmentation. However, due to the computational demands of these approaches, …

We propose a random graph model which is a special case of sparse random graphs with
given degree sequences. This model involves only a small number of parameters, called …

We 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 …

A local graph partitioning algorithm finds a cut near a specified starting vertex, with a running
time that depends largely on the size of the small side of the cut, rather than the size of the …

We examine a number of generalized and extended versions of concentration inequalities
and martingale inequalities. These inequalities are effective for analyzing processes with …

We study discrete Green's functions and their relationship with discrete Laplace equations.
Several methods for deriving Green's functions are discussed. Green's functions can be used …

Random graph theory is used to examine the “small-world phenomenon”; any two strangers
are connected through a short chain of mutual acquaintances. We will show that for certain …

In the study of the spectra of power-law graphs, there are basically two competing approaches.
One is to prove analogues of Wigner's semicircle law, whereas the other predicts that the …

This paper considers the following game on a hypercube, first suggested by Lagarias and
Saks. Suppose $2^n$ pebbles are distributed onto vertices of an n-cube (with $2^n$ vertices). …

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 …