The graph is a critical and useful concept in designing many information processing systems. Systems such as transaction processing systems, decision support systems, and workflow systems are all helped immensely by a graphical structure. Simple graphs and digraphs allow for the construction of a variety of system design tools that provide a convenient and appealing format for illustrating information infrastructures, while allowing any subsequent analyses to be performed by the user. However, the metagraph, a new graphical structure that is developed in this book, goes beyond the representational and provides Information Systems with a robust, analytical modeling graphic tool. METAGRAPHS AND THEIR APPLICATIONS is a presentation of metagraph theory and its applications that begins by defining a metagraph and its uses. They are more complex than a simple graph structure, but they allow for representation and analysis of more complex systems. The material contained in this book is presented in two parts. The first develops the theoretical results with the emphasis on the development of a metagraph algebra. In the second part of the book, four promising applications of metagraphs are examined: 1) modeling of data relations, 2) the modeling of decision models, 3) the modeling of decision rules, and 4) the modeling of workflow tasks. Hence, the theoretical results in the initial chapters lay the foundation for the application areas in the second part of the book. The book concludes by examining several possible extensions of this work. Of special interest is the structuring of the metagraphs modeling process, which may enhance the body of work on systems analysis and design (including software engineering), the development of a metagraphs workbench to support such a process, and the possible application of the results presented here, suitably enhanced, to social networks.