Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University. Chung's well-written exposition can be likened to a conversation with a good teacher--one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. The monograph is accessible to the nonexpert who is interested in reading about this evolving area of mathematics.

Review

The book presents a very complete picture of how various properties of a graph--from Cheeger constants and diameters to more recent developments such as log-Sobolev constants and Harnack inequalities--are related to the spectrum. Even though the point of view of the book is quite geometric, the methods and exposition are purely graph-theoretic. As a result, the book is quite accessible to a reader who does not have any background in geometry. As the author writes, `the underlying mathematics of spectral graph theory through all its connections to the pure and applied, the continuous and discrete, can be viewed as a single unified subject.' Anyone who finds this sentence appealing is encouraged to give this book a try. He or she will not be disappointed. ---- Mathematical Reviews

Incorporates a great deal of recent work, much of it due to the author herself ... clear, without being pedantic, and challenging, without being obscure. ---- Bulletin of the London Mathematical Society

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