Stat Papers DOI 10.1007/s00362-017-0961-1 BOOK REVIEW

Ernesto Estrada and Philip A. Knight (2015): A First Course in Network Theory, Oxford University Press, 272 pp., £29.99, ISBN 9780198726463 Karl Mosler1

Received: 6 October 2017 / Revised: 11 October 2017 © Springer-Verlag GmbH Germany 2017

Networks arise in many fields, such as Physics, Sociology and Genetics, and various models of random graphs and networks have been developed for their statistical analysis. Specifically, network edges may describe physical or social interactions, spatial closeness, or functional dependences. Typical tasks include the propagation of activities, the detection of local clusters, and the identification of leading positions in the network. The present book provides an introduction to the theory of network models with a focus on applications; it is directed to students and researchers in quantitative disciplines and starts with short accounts of graph theory, proof techniques, and data analysis (Chapters 1 to 4). Then the algebraic approach to networks is developed (Chapters 5 to 7), which is employed throughout the rest of the text. Basic notions are the adjacency matrix and the Laplacian of a graph, their eigenvectors and eigenvalues. In the sequel, complex networks are characterized in probabilistic terms, and several models of random networks are introduced, which differ in certain characteristics such as their degree distribution and their clustering coefficient (Chapters 9 to 11). Chapters 12 to 15 then cover the identification of subgraphs and the centrality of vertices. Various global properties of networks such as the assortativity of nodes, reciprocity of paths, or communicability between nodes, are addressed in Chapters 17 to 19. The final Chapter 21 is about the identification of communities, that is, special local clusters. To illustrate the use of theory for applied work, the authors exhibit analogies in classical physics—mechanical and electrical networks—, in quantum mechanics and in statistical physics (Chapters 8, 16, and 20).

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Karl Mosler [email protected] Institute of Econometrics and Statistics Universität zu Köln, Köln, Germany

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K. Mosler

The authors are to be congratulated for this fresh and motivating textbook, which provides a sound mathematical understanding of modern network theory and enables the reader to cope with practical applications in various fields. The material is presented in a simple but always precise style, and it is illustrated with plenty of examples and didactical elements. Most of the text has no prerequisites besides elementary algebra. So, the book is readily accessible for any researcher who is interested in applying network models to his or her field of inquiry. For students of mathematics or statistics the book may be used in their last undergraduate year, for students of other quantitative disciplines in their graduate studies.

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