Graphs are usually represented as geometric objects drawn in the
plane, consisting of nodes and curves connecting them. The main
message of this book is that such a representation is not merely a way
to visualize the graph, but an important mathematical tool. It is
obvious that this geometry is crucial in engineering, for example, if
you want to understand rigidity of frameworks and mobility of
mechanisms. But even if there is no geometry directly connected to the
graph-theoretic problem, a well-chosen geometric embedding has
mathematical meaning and applications in proofs and algorithms. This
book surveys a number of such connections between graph theory and
geometry: among others, rubber band representations, coin
representations, orthogonal representations, and discrete analytic
functions. Applications are given in information theory, statistical
physics, graph algorithms and quantum physics.

The book is based on courses and lectures that the author has given
over the last few decades and offers readers with some knowledge of
graph theory, linear algebra, and probability a thorough introduction
to this exciting new area with a large collection of illuminating
examples and exercises.

*Geometric representations of graphs lead to
significant insights in the study of graph properties and their
algorithmic aspects. This book is a thorough study of the subject
written by the pioneer of many of the results in the area. It is a
fascinating manuscript written by a superb mathematician who is also a
fantastic expositor.*

—**Noga Alon, Princeton University and Tel
Aviv University**

*A beautiful book, rich in intuition, insights,
and examples, from one of the masters of combinatorics, geometry, and
graph theory. This book presents old friends of graph theory in a new
light and introduces more recent developments, providing connections
to many areas in combinatorics, analysis, algorithms, and
physics. Those of us who know graph theory still have much to learn
from this presentation; for those who are new to the field, the book
is a wonderful gift and invitation to participate.*

—**Jennifer Chayes, Microsoft Research**

*László Lovász is one of the
most prominent experts in discrete mathematics. The book is unique and
inspiring for students and researchers as well. The author succeeded
to show the wealth and beauty of the subject.*

—**Endre Szemerédi, Rutgers
University **

Readership

Graduate students and researchers interested in graph
theory.