Network Models

Abstract

Graph theory, the subject at the root of this chapter, dates back to 1736, when the Swiss mathematician Leonard Euler considered the now famed “Königsberg bridge problem.” At that time, there were seven bridges across the River Pregel that ran through the city of Königsberg on the Baltic Sea, and Euler wondered whether or not it would be possible to start somewhere in the city, walk across each of the bridges exactly once, and return to where he came from. (It was not). We will return to Euler’s problem in Section 5.5 of this chapter. Two hundred years later in 1936, the Hungarian mathematician Denès König wrote the seminal book “The Theory of Finite and Infinite Graphs,” that laid the foundations of modern graph theory. The subject was first used by operations researchers in the 1950s, most prominently by L.R. Ford and D.R. Fulkerson.