# Graph theory

**DOI:**https://doi.org/10.1007/1-4020-0611-X_402

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## INTRODUCTION

Graph theory is the general study of the interconnection of various elements. While the origins of graph theory can be traced back to the eighteenth century, this area of discrete mathematics has experienced most of its tremendous growth during the past few decades. This rapid growth, both in the development of new theory and applications, reflects the fact that graphs can model a wide variety of natural and technological systems.

A number of physical systems can be viewed as *graphs*, composed of *nodes* (or vertices) connected together by *edges*(or arcs). For example, a local area computer network defines a graph whose nodes represent individual computers (or peripheral devices) and whose edges represent the physical cables connecting such computers. A telecommunication net-work consists of telephone locations (and central switching stations) joined by sections of copper wire (and optical fibers); an airline system has airports as its nodes and direct flights as its edges;...

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