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- Fan R. K. Chung, Linyuan Lu
- Proceedings of the National Academy of Sciencesâ€¦
- 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 randomâ€¦ (More)

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.â€¦ (More)

- Fan R. K. 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 aâ€¦ (More)

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.â€¦ (More)

We study the graph-theoretic problem of embedding a graph in a book with its vertices in a line along the spine of the book and its edges on the pages in such a way that edges residing on the sameâ€¦ (More)

- Fan R. K. Chung, Linyuan Lu, Van V Vu
- Proceedings of the National Academy of Sciencesâ€¦
- 2003

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 eigenvaluesâ€¦ (More)

- Fan R. K. 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 forâ€¦ (More)

- Fan R. K. 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, withâ€¦ (More)

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

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 diameter ofâ€¦ (More)