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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 input graph. In this paper, we present an algorithm for local graph partitioning using personalized PageRank vectors. We develop an improved algorithm for computing… (More)

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 logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from these parameters, various properties of the graph can be… (More)

Spectral graph theoretic methods have recently shown great promise for the problem of image segmentation. However, due to the computational demands of these approaches, applications to large problems such as spatiotemporal data and high resolution imagery have been slow to appear. The contribution of this paper is a method that substantially reduces the… (More)

We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this class.

Optical Orthogonal codes; design analysis and applications – p. 1/33

A classical topic in combinatorics is the study of problems of the following type: What are the maximum families F of subsets of a finite set with the property that the intersection of any two sets in the family satisfies some specified condition? Typical restrictions on the intersections F n F of any F and F' in F are: (i) FnF'# 0, where all FEF have k… (More)

For every E > 0 and every integer m > 0, we construct explicitly graphs with O(m/e) vertices and maximum degree 0(1/e*), such that after removing any (1-l) portion of their vertices or edges, the remaining graph still contains a path of length m. This settles a problem of Rosenberg, which was motivated by the study of fault torerant linear arrays.

In this paper, we examine a spectral clustering algorithm for similarity graphs drawn from a simple random graph model, where nodes are allowed to have varying degrees, and we provide theoretical bounds on its performance. The random graph model we study is the Extended Planted Partition (EPP) model, a variant of the classical planted partition model. The… (More)

Many massive graphs (such as WWW graphs and Call graphs) share certain universal characteristics which can be described by so-called the " power law ". In this paper, we will first briefly survey the history and previous work on power law graphs. Then we will give four evolution models for generating power law graphs by adding one node/edge at a time. We… (More)

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 families of random graphs with given expected degrees, the average distance is almost surely of order log n/ log˜d where˜d is the weighted average of the sum of squares of the… (More)