Hybrid Graph Theory and Network Analysis
Hybrid Graph Theory and Network Analysis by Ladislav Novak, published by Cambridge University Press on September 3, 2009, offers a comprehensive exploration of the intersection between traditional graph theory and matroid theory. This 188-page book presents a mathematical approach to network analysis, focusing on the dual structures of circuits and cutsets that are integral to understanding graphs. The text introduces a hybrid structure known as a graphoid, which is essential for analyzing networks and represents a significant advancement in the field.
Readers will find that this book synthesizes over thirty years of research, providing new results and insights into hybrid graph theory. It delves into the relationships between circuits and cutsets, emphasizing their interdependence and relevance to network analysis. Aimed at mathematicians, computer scientists, and electrical engineers, this edition serves as a definitive resource for those engaged in theoretical network analysis, presenting a thorough examination of the subject matter.
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This book combines traditional graph theory with the matroid view of graphs in order to throw light on the mathematical approach to network analysis. The authors examine in detail two dual structures associated with a graph, namely circuits and cutsets. These are strongly dependent on one another and together constitute a third, hybrid, vertex-independent structure called a graphoid, whose study is here termed hybrid graph theory. This approach has particular relevance for network analysis. The first account of the subject in book form, the text includes many new results as well as the synthesizing and reworking of much research done over the past thirty years (historically, the study of hybrid aspects of graphs owes much to the foundational work of Japanese researchers). This work will be regarded as the definitive account of the subject, suitable for all working in theoretical network analysis: mathematicians, computer scientists or electrical engineers.
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