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- Fan Chung
- 2005

We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a… (More)

- Fan Chung, Linyuan Lu
- 2002

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 degrees of its endpoints.… (More)

- Fan Chung, Linyuan Lu
- Proceedings of the National Academy of Sciences…
- 2002

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… (More)

- Fan Chung
- 2006

Contents Preface vii Chapter 1. Graph Theory in the Information Age 1 1.1. Introduction 1 1.2. Basic definitions 3 1.3. Degree sequences and the power law 6 1.4. History of the power law 8 1.5.… (More)

- Fan Chung
- 2007

The concept of pagerank was first started as a way for determining the ranking of Webpages by Web search engines. Based on relations in interconnected networks, pagerank has become a major tool for… (More)

- Fan Chung, SHIRIN HANDJANI, DOUG JUNGREIS
- 2003

We consider generalizations of the classical Polya urn problem: Given finitely many bins each containing one ball, suppose that additional balls arrive one at a time. For each new ball, with… (More)

- Fan Chung, Linyuan Lu
- 2005

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

- Fan Chung, Linyuan Lu, Van Thuc Vu
- 2003

Many graphs arising in various information networks exhibit the “power law” behavior — the number of vertices of degree k is proportional to k−β for some positive β. We show that if β > 2.5, the… (More)

For a specified subset S of vertices in a graph G we consider local cuts that separate a subset of S. We consider the local Cheeger constant which is the minimum Cheeger ratio over all subsets of S,… (More)

- Fan Chung, Linyuan Lu
- 2000

Abstract We consider the diameter of a random graph G(n, p) for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the… (More)