The Analyst's Bookshelf.

This article focuses on the book "Theorie des Graphes et ses Applications," by Claude Berge. The term graph, the subject of this book has not the common connotation of a plot or curve, but refers to an established but esoteric mathematical sage. The geometric aspect of the above definition is not the heart of the matter, graphs can be symbolic diagrams of a rich variety of situations. The points can represent almost any kind of object and the arcs almost any type of interrelation between them. There is a chapter on transportation networks in the book. It includes Ford-Fulkerson algorithms and the theorems of Hoffman and Gale. Besides questions of optimizing transport and routing the same techniques are fitted to the problem of minimal covering, some combinational teasers, problems in a set theory, and linear programming are also given. The methods continue to solve problems in some subsequent chapters. In what are called simple graphs, the vertices are divided into two sets such that all arcs connect only members of one set with points of the other.