About this item
Highlights
- Graphs and Networks A unique blend of graph theory and network science for mathematicians and data science professionals alike.
- About the Author: S. R. Kingan is an Associate Professor of Mathematics at Brooklyn College and the Graduate Center of The City University of New York.
- 288 Pages
- Mathematics, Number Theory
Description
About the Book
"Network science is applied graph theory, and this book successfully blends essential graph theory topics with practical and relevant network science to illustrate the underlying mathematics. Mathematicians have been relegated to small-time players in a field populated with sociologists, computer scientists, and physicists. On the other hand, graph theory books are written like reference manuals jam-packed with theorems for graph theorists, leading instructors of graph theory courses to tease out their lectures from a plethora of results. This book's combination of theory and modern applications is needed by both practitioners of data science and students of graph theory seeking to learn modern applications. For example, one difference between this book and existing network science books is that network scientists title their chapters based on individual large graphs such as epidemic graphs or web graphs and study all its properties. However, large graphs have a lot of features in common so this book distills those common elements, presents the concepts behind the large graphs, and presents particular large graphs as examples of the underlying mathematics. With a focus on topics most relevant to network science, such as graph structural theory, link analysis, and spectral graph theory, this book contains a host of untapped results for network scientists. In addition, the book is supplemented with a related website and an Instructor's Manual. Topical coverage includes: basic definitions; isomorphism; graph substructures; graph operations; graph statistics; tress; degree sequences; Eulerian circuits; Hamiltonian cycles; planar graphs; colorings; matchings and coverings; graph algorithms; network algorithms; random graphs; spectral graph theory; centrality measures; network flows; network reliability; extremal graph theory; higher connectivity; excluded minors; Tutte's wheels theorem; splitter theorem; and k-sums and decomposition"--Book Synopsis
Graphs and NetworksA unique blend of graph theory and network science for mathematicians and data science professionals alike.
Featuring topics such as minors, connectomes, trees, distance, spectral graph theory, similarity, centrality, small-world networks, scale-free networks, graph algorithms, Eulerian circuits, Hamiltonian cycles, coloring, higher connectivity, planar graphs, flows, matchings, and coverings, Graphs and Networks contains modern applications for graph theorists and a host of useful theorems for network scientists.
The book begins with applications to biology and the social and political sciences and gradually takes a more theoretical direction toward graph structure theory and combinatorial optimization. A background in linear algebra, probability, and statistics provides the proper frame of reference.
Graphs and Networks also features:
- Applications to neuroscience, climate science, and the social and political sciences
- A research outlook integrated directly into the narrative with ideas for students interested in pursuing research projects at all levels
- A large selection of primary and secondary sources for further reading
- Historical notes that hint at the passion and excitement behind the discoveries
- Practice problems that reinforce the concepts and encourage further investigation and independent work
From the Back Cover
A unique blend of graph theory and network science for mathematicians and data science professionals alike.
Featuring topics such as minors, connectomes, trees, distance, spectral graph theory, similarity, centrality, small-world networks, scale-free networks, graph algorithms, Eulerian circuits, Hamiltonian cycles, coloring, higher connectivity, planar graphs, flows, matchings, and coverings, Graphs and Networks contains modern applications for graph theorists and a host of useful theorems for network scientists.
The book begins with applications to biology and the social and political sciences and gradually takes a more theoretical direction toward graph structure theory and combinatorial optimization. A background in linear algebra, probability, and statistics provides the proper frame of reference.
Graphs and Networks also features:
- Applications to neuroscience, climate science, and the social and political sciences
- A research outlook integrated directly into the narrative with ideas for students interested in pursuing research projects at all levels
- A large selection of primary and secondary sources for further reading
- Historical notes that hint at the passion and excitement behind the discoveries
- Practice problems that reinforce the concepts and encourage further investigation and independent work
About the Author
S. R. Kingan is an Associate Professor of Mathematics at Brooklyn College and the Graduate Center of The City University of New York. Dr. Kingan's research interests include graph theory, matroid theory, combinatorial algorithms, and their applications.