Structural Models [antikvár]

Preface I see no good reasons why the views given in this volume should shock the religious feelings of anyone. Charles Darwin On the Origin of Species by Means of Natural Selection The purpose of this book is to present an introduction to a body of mathematics concerned with the abstract notion of "structure." Its preparation has been motivated by the belief that knowledge of the mathematics of abstract structures will be of value to investigators interested in various kinds of empirical structures. The mathematics with which we are concerned is known as the theory of directed graphs, or more briefly as digraph theory. It deals with abstract configurations called digraphs, which consist of "points" and "directed lines." When these terms are given concrete referents, digraphs serve as mathematical models of empirical structures, and properties of digraphs reflect structural properties of the empirical world. Since the same mathematical terms can be given a variety of empirical meanings, digraph theory has applicability to many different fields of investigation. The authors of this book, two mathematicians and a psychologist, have collaborated over a period of years in an attempt to develop a theory of digraphs that will reveal as clearly as possible its potential usefulness to the empirical investigator. In addition to organizing the known results about digraph theory, we have endeavored to fill a few of the gaps in the existing mathematical literature. In this work, we have addressed ourselves primarily to structural phenomena of interest to social scientists. We believe, however, that the material will also be of value to those working with computers, programming, information retrieval, automata, linguistics, cryptology, and electrical engineering. One attractive feature of digraph theory for the nonmathematician is its relatively self-contained nature. The mathematical training acquired