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The Nature of Complex Networks provides a systematic introduction to the statistical mechanics of complex networks and the different theoretical achievements in the field that are now finding strands in common. The book presents a wide range of networks and the processes taking place on them, including recently developed directions, methods, and techniques. It assumes a statistical mechanics view of random networks based on the concept of statistical ensembles but also features the approaches and methods of modern random graph theory and their overlaps with statistical physics. This book will appeal to graduate students and researchers in the fields of statistical physics, complex systems, graph theory, applied mathematics, and theoretical epidemiology.
Preface.
First Insight.
Graphs.
Classical Random Graphs.
Equilibrium Networks.
Evolving Networks.
Connected Components.
Epidemics and Spreading Phenomena.
Networks of Networks.
Spectra and Communities.
Walks and Search.
Cooperative Systems on Networks 356
Inference and Reconstruction 374
What’s Next ?
Further reading.
Appendix A Adjacency Matrix for Hypergraphs.
Appendix B Spectra of symmetric normalized Laplacians of sample graphs.
Appendix C Generating Functions.
Appendix D Hyperscaling Relations for Percolation.
Appendix E Degree Distribution of a Damaged Network.
Appendix F Non-backtracking Matrix.
Appendix G Treating General Interdependent Networks.
References.
Index