Frank Harary – författare

In their previous book, Structural Models in Anthropology, anthropologist Per Hage and mathematician Frank Harary used graph theory, a branch of pure mathematics, to develop a family of models for the study of social, symbolic, and cognitive relations.In this book the authors extend these models and apply them to the analysis of exchange structures in Oceania, presenting graph theory in a form accessible to the non-mathematical reader. Using ethnographic data from Melanesia, Micronesia, and Polynesia, they demonstrate that the language, techniques, and theorems of graph theory provide the essential basis for the description, quantification, simulation, enumeration, and notation of the great variety of exchange forms actually found in Oceanic societies.

An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.

An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.

An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.

An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.

Contrary to common perception and belief, most island societies of the Pacific were not isolated, but were connected to other island societies by relations of kinship and marriage, trade and tribute, language and history. Using network models from graph theory, the authors analyse the formation of island empires, the social basis of dialect groups, the emergence of economic and political centres, the evolution and devolution of social stratification and the evolution of kinship terminologies, marriage systems and descent groups from common historical prototypes. The book is at once a unique and important contribution to Oceania studies, anthropology and social network analysis.

Hage and Harary present a comprehensive introduction to the use of graph theory in social and cultural anthropology. Using a wide range of empirical examples, the authors illustrate how graph theory can provide a language for expressing in a more exact fashion concepts and notions that can only be imperfectly rendered verbally. They show how graphs, digraphs and networks, together with their associated matrices and duality laws, facilitate the study of such diverse topics as mediation and power in exchange systems, reachability in social networks, efficiency in cognitive schemata, logic in kinship relations, and productivity in subsistence modes. The interaction between graphs and groups provides further means for the analysis of transformations in myths and permutations in symbolic systems. The totality of these structural models aids in the collection as well as the interpretation of field data. The presentation is clear, precise and readily accessible to the nonmathematical reader. It emphasizes the implicit presence of graph theory in much of anthropological thinking.

Contrary to common perception and belief, most island societies of the Pacific were not isolated, but were connected to other island societies by relations of kinship and marriage, trade and tribute, language and history. Using network models from graph theory, the authors analyse the formation of island empires, the social basis of dialect groups, the emergence of economic and political centres, the evolution and devolution of social stratification and the evolution of kinship terminologies, marriage systems and descent groups from common historical prototypes. The book is at once a unique and important contribution to Oceania studies, anthropology and social network analysis.

Graphical Enumeration deals with the enumeration of various kinds of graphs. Topics covered range from labeled enumeration and George Pólya''s theorem to rooted and unrooted trees, graphs and digraphs, and power group enumeration. Superposition, blocks, and asymptotics are also discussed. A number of unsolved enumeration problems are presented. Comprised of 10 chapters, this book begins with an overview of labeled graphs, followed by a description of the basic enumeration theorem of Pólya. The next three chapters count an enormous variety of trees, graphs, and digraphs. The Power Group Enumeration Theorem is then described together with some of its applications, including the enumeration of self-complementary graphs and digraphs and finite automata. Two other chapters focus on the counting of superposition and blocks, while another chapter is devoted to asymptotic numbers that are developed for several different graphical structures. The book concludes with a comprehensive definitive list of unsolved graphical enumeration problems. This monograph will be of interest to both students and practitioners of mathematics.