Complex Networks Principles, Methods and Applications Networks constitute the backbone of complex systems, from the human brain to computer communications, transport infrastructures to online social systems, metabolic reactions to financial markets Characterising their structure improves our understanding of the physical, biological, economic and social phenomena that shape our world Rigorous and thorough, this textbook presents a detailed overview of the new theory and methods of network science Covering algorithms for graph exploration, node ranking and network generation, among the others, the book allows students to experiment with network models and real-world data sets, providing them with a deep understanding of the basics of network theory and its practical applications Systems of growing complexity are examined in detail, challenging students to increase their level of skill An engaging presentation of the important principles of network science makes this the perfect reference for researchers and undergraduate and graduate students in physics, mathematics, engineering, biology, neuroscience and social sciences Vito Latora is Professor of Applied Mathematics and Chair of Complex Systems at Queen Mary University of London Noted for his research in statistical physics and in complex networks, his current interests include time-varying and multiplex networks, and their applications to socio-economic systems and to the human brain Vincenzo Nicosia is Lecturer in Networks and Data Analysis at the School of Mathematical Sciences at Queen Mary University of London His research spans several aspects of network structure and dynamics, and his recent interests include multi-layer networks and their applications to big data modelling Giovanni Russo is Professor of Numerical Analysis in the Department of Mathematics and Computer Science at the University of Catania, Italy, focusing on numerical methods for partial differential equations, with particular application to hyperbolic and kinetic problems 22:00:51, subject to the Cambridge Core terms of use, 22:00:51, subject to the Cambridge Core terms of use, Complex Networks Principles, Methods and Applications VITO LATOR A Queen Mary University of London VINCENZO NICOSIA Queen Mary University of London GIOVANNI RUSSO University of Catania, Italy 22:00:51, subject to the Cambridge Core terms of use, University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 4843/24, 2nd Floor, Ansari Road, Daryaganj, Delhi – 110002, India 79 Anson Road, #06–04/06, Singapore 079906 Cambridge University Press is part of the University of Cambridge It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence www.cambridge.org Information on this title: www.cambridge.org/9781107103184 DOI: 10.1017/9781316216002 © Vito Latora, Vincenzo Nicosia and Giovanni Russo 2017 This publication is in copyright Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published 2017 Printed in the United Kingdom by TJ International Ltd Padstow Cornwall A catalogue record for this publication is available from the British Library Library of Congress Cataloging-in-Publication Data Names: Latora, Vito, author | Nicosia, Vincenzo, author | Russo, Giovanni, author Title: Complex networks : principles, methods and applications / Vito Latora, Queen Mary University of London, Vincenzo Nicosia, Queen Mary University of London, Giovanni Russo, Università degli Studi di Catania, Italy Description: Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2017 | Includes bibliographical references and index Identifiers: LCCN 2017026029 | ISBN 9781107103184 (hardback) Subjects: LCSH: Network analysis (Planning) Classification: LCC T57.85 L36 2017 | DDC 003/.72–dc23 LC record available at https://lccn.loc.gov/2017026029 ISBN 978-1-107-10318-4 Hardback Additional resources for this publication at www.cambridge.org/9781107103184 Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate 22:00:51, subject to the Cambridge Core terms of use, To Giusi, Francesca and Alessandra 22:03:03, subject to the Cambridge Core terms of use, 22:03:03, subject to the Cambridge Core terms of use, Contents Preface Introduction The Backbone of a Complex System Complex Networks Are All Around Us Why Study Complex Networks? Overview of the Book Acknowledgements Graphs and Graph Theory 1.1 What Is a Graph? 1.2 Directed, Weighted and Bipartite Graphs 1.3 Basic Definitions 1.4 Trees 1.5 Graph Theory and the Bridges of Königsberg 1.6 How to Represent a Graph 1.7 What We Have Learned and Further Readings Problems Centrality Measures 2.1 The Importance of Being Central 2.2 Connected Graphs and Irreducible Matrices 2.3 Degree and Eigenvector Centrality 2.4 Measures Based on Shortest Paths 2.5 Movie Actors 2.6 Group Centrality 2.7 What We Have Learned and Further Readings Problems Random Graphs 3.1 3.2 3.3 3.4 3.5 3.6 Erd˝os and Rényi (ER) Models Degree Distribution Trees, Cycles and Complete Subgraphs Giant Connected Component Scientific Collaboration Networks Characteristic Path Length page xi xii xii xiv xv xvii xx 1 13 17 19 23 28 28 31 31 34 39 47 56 62 64 65 69 69 76 79 84 90 94 vii 22:05:41, subject to the Cambridge Core terms of use, Contents viii 3.7 What We Have Learned and Further Readings Problems 103 104 Small-World Networks 107 107 112 116 127 135 144 148 148 4.1 Six Degrees of Separation 4.2 The Brain of a Worm 4.3 Clustering Coefficient 4.4 The Watts–Strogatz (WS) Model 4.5 Variations to the Theme 4.6 Navigating Small-World Networks 4.7 What We Have Learned and Further Readings Problems Generalised Random Graphs 5.1 The World Wide Web 5.2 Power-Law Degree Distributions 5.3 The Configuration Model 5.4 Random Graphs with Arbitrary Degree Distribution 5.5 Scale-Free Random Graphs 5.6 Probability Generating Functions 5.7 What We Have Learned and Further Readings Problems Models of Growing Graphs 6.1 Citation Networks and the Linear Preferential Attachment 6.2 The Barabási–Albert (BA) Model 6.3 The Importance of Being Preferential and Linear 6.4 Variations to the Theme 6.5 Can Latecomers Make It? The Fitness Model 6.6 Optimisation Models 6.7 What We Have Learned and Further Readings Problems Degree Correlations 7.1 The Internet and Other Correlated Networks 7.2 Dealing with Correlated Networks 7.3 Assortative and Disassortative Networks 7.4 Newman’s Correlation Coefficient 7.5 Models of Networks with Degree–Degree Correlations 7.6 What We Have Learned and Further Readings Problems Cycles and Motifs 8.1 8.2 8.3 Counting Cycles Cycles in Scale-Free Networks Spatial Networks of Urban Streets 151 151 161 171 178 184 188 202 204 206 206 215 224 230 241 248 252 253 257 257 262 268 275 285 290 291 294 294 303 307 22:05:41, subject to the Cambridge Core terms of use, Contents ix 8.4 Transcription Regulation Networks 8.5 Motif Analysis 8.6 What We Have Learned and Further Readings Problems 316 324 329 330 Community Structure 332 332 336 342 349 354 357 365 369 371 9.1 Zachary’s Karate Club 9.2 The Spectral Bisection Method 9.3 Hierarchical Clustering 9.4 The Girvan–Newman Method 9.5 Computer Generated Benchmarks 9.6 The Modularity 9.7 A Local Method 9.8 What We Have Learned and Further Readings Problems 10 Weighted Networks 374 374 381 387 393 401 407 408 10.1 Tuning the Interactions 10.2 Basic Measures 10.3 Motifs and Communities 10.4 Growing Weighted Networks 10.5 Networks of Stocks in a Financial Market 10.6 What We Have Learned and Further Readings Problems Appendices A.1 A.2 A.3 A.4 A.5 A.6 A.7 A.8 A.9 A.10 A.11 A.12 A.13 A.14 A.15 A.16 A.17 A.18 A.19 Problems, Algorithms and Time Complexity A Simple Introduction to Computational Complexity Elementary Data Structures Basic Operations with Sparse Matrices Eigenvalue and Eigenvector Computation Computation of Shortest Paths Computation of Node Betweenness Component Analysis Random Sampling Erd˝os and Rényi Random Graph Models The Watts–Strogatz Small-World Model The Configuration Model Growing Unweighted Graphs Random Graphs with Degree–Degree Correlations Johnson’s Algorithm to Enumerate Cycles Motifs Analysis 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Albert, 260 De Los Rios, Paolo, 137, 203 de Solla Price, Derek, 214, 224 Di Matteo, Tiziana, 408 Dorogovtsev, Sergey, 230, 397 Durrett, Rick, 179 Babiloni, Fabio, 116 Bacon, Kevin, 110 Baiesi, Marco, 407 Barabási, Albert-László, xv, 152, 153, 215, 232, 243, 499 Barrat, Alain, 284, 381, 394 Barthélemy, Marc, 241, 329, 370, 381, 394 Bavelas, Alex, 33 Bender, Edward, 171 Bergstrom, Carl, 370 Berners-Lee, Tim, 152 Bianconi, Ginestra, 243, 305, 306 Blanchard, Philippe, 329 Blondel, Vincent, 370 Boccaletti, Stefano, 252 Boguñá, Marián, 148, 187, 204, 260, 266, 285 Bollobás, Béla, 28, 84, 104, 171 Bonacich, Phillip, 41 Bonanno, Giovanni, 401, 403 Borgatti, Steve, 62 Brandes, Ulrik, 462 Brenner, Sydney, 112 Broder, Andrei, 169 Bullmore, Ed, 116, 148 Burt, Ronald Stuart, 149 Erd˝os, Paul, 69, 111 Estrada, Ernesto, 296 Euler, Leonhard, 1, 19, 28 Evans, Tim, 229 Everett, Martin, 62 Caldarelli, Guido, 203, 306 Canfield, Rodney, 171 Capocci, Andrea, 203, 306 Cardillo, Alessio, 407 Cayley, Arthur, Chavez, Mario, 116 Chung, Fan, 185 Clauset, Aaron, 519 Cohen, Reuven, 185 Colizza, Vittoria, 272, 376, 385 Crucitti, Paolo, 308 D’Souza, Raissa, 248 Fagiolo, Giorgio, 407 Faust, Katherine, 65 Fernandez, Alberto, 370 Ferrer i Cancho, Ramon, 255 Fiedler, Miroslav, 340 Fisher, Ronald, 343 Flammini, Alessandro, 272 Fortunato, Santo, 357, 370 Freeman, Linton, 49 Frobenius, Georg, 42 Gómez, Sergio, 370 Gómez-Gardes, Jesús, 241 Garlaschelli, Diego, 10, 407 Ginsparg, Paul, 91 Girvan, Michelle, 349 Goh, Kwang-Il, 203 Golub, Gene, 446 Granovetter, Mark, 129, 400 Guillame, Jean-Loup, 370 Guimerá, Roger, 353 Harary, Frank, 28 Havlin, Shlomo, 185 Hierholzer, Carl, 21 Hirsch, Jorge Eduardo, 212 Holme, Petter, 223 Isaacson, Eugene, 451 Jackson, Matthew, 65 Jacobs, Allan, 308 Jeong, Hawoong, 152, 153 Johnson, Donald, 508 550 22:10:54, subject to the Cambridge Core terms of use, Author Index 551 Johnson, Stephen C., 344 Kahng, Byungnam, 203 Kaiser, Marcus, 148 Kaski, Kimmo, 387, 398 Katz, Leo, 295, 348 Keller, Herbert Bishop, 451 Kertész, Janos, 387, 398 Kim, Beom Jun, 223 Kim, Doochul, 203 Kirchhoff, Gustav, Kleinberg, Jon, 142, 144, 160 Knuth, Donald Ervin, 410 Kosaraju, Sambasiva, 473 Krapivsky, Pavel, 228, 236, 282, 393 Kruskal, Joseph, 405, 528 Kumara, Soundar, 365 Kumpula, Jouko, 398 Kuratowski, Kasimir, 312 Lacasa, Lucas, 408 Lambiotte, Renaud, 370 Lancichinetti, Andrea, 357 Latora, Vito, 52, 123, 308, 407 Leavitt, Harold, 33 Lefebvre, Etienne, 370 Leskovec, Jure, 153 Leyvraz, Francois, 228 Liben-Nowell, David, 147 Lillo, Fabrizio, 401, 403 Loffredo, Maria, 10 Lu, Lin Yuan, 185 Luque, Bartolo, 408 Ma, Athen, 407 Mantegna, Rosario, 401, 403, 408 Marchiori, Massimo, 52, 123 Marsili, Matteo, 305 Mendes, José, 230, 397 Milgram, Stanley, 107 Molloy, Michael, 179 Mondragón, Rẳl, 407 Moore, Christopher, 519 Moreno, Yamir, 241 Muñoz, Miguel, 203 Newman, Mark, 90, 91, 106, 137, 188, 195, 204, 278, 287, 349, 363, 370, 375, 519 Nicosia, Vincenzo, 148 Panzarasa, Pietro, 385 Pastor-Satorras, Romualdo, 187, 262, 266, 269, 284, 285, 291, 376, 381 Perron, Oskar, 42 Persson, Olle, 208 Petermann, Thomas, 137 Porta, Sergio, 308, 407 Rényi, Alfréd, 69 Radicchi, Filippo, 357 Raghavan, Usha, 365 Ramasco, José, 385 Rapoport, Anatol, 203 Redner, Sidney, 208, 228, 236, 282 Reed, Bruce, 179 Rodgers, Geoff, 236 Rodríguez-Velázquez, Juan, 296 Rosvall, Martin, 370 Saad, Yousuf, 451 Samukhin, A.N., 230 Saramäki, Jari, 229, 387, 398 Scala, Antonio, 241 Scellato, Salvatore, 407 Scott, John, 65 Serrano, M Ángeles, 148, 204, 260, 272 Sharir, Micha, 473 Simon, Herbert, 225 Solè, Ricard, 255 Sporns, Olaf, 116, 148 Stanley, H Eugene, 80, 241 Strano, Emanuele, 329 Strogatz, Steven, xv, 57, 128, 188, 489 Tarjan, Robert, 472 Tieri, Paolo, 407 Tumminello, Michele, 408 Turing, Alan, 421 Vázquez, Alexei, 229, 262, 269 Vértes, Petra, 148 Van Loan, Charles, 446 Varier, Sreedevi, 148 Vespignani, Alessandro, 187, 262, 267, 269, 272, 291, 376, 381, 394 Volchenkov, Dimitri, 329 Wasserman, Stanley, 65 Watts, Duncan, xv, 57, 128, 137, 188, 489 West, Douglas B., 28 Onnela, Jukka-Pekka, 387, 398 Opshal, Tore, 385 Yule, G Udny, 225 Paczuski Maya, 407 Zachary, Wayne, 332, 392 22:10:54, subject to the Cambridge Core terms of use, ... of a Complex System Complex Networks Are All Around Us Why Study Complex Networks? Overview of the Book Acknowledgements Graphs and Graph Theory 1.1 What Is a Graph? 1.2 Directed, Weighted and. .. the 1998 Watts and Strogatz (WS) article on small-world networks and by the 1999 Barabási and Albert (BA) article on scale-free networks Right panel: number of papers on complex networks that...22:00:51, subject to the Cambridge Core terms of use, Complex Networks Principles, Methods and Applications VITO LATOR A Queen Mary University of London VINCENZO NICOSIA