Scale-free networks : complex webs in nature and technology / / Guido Caldarelli

• Record Nr.: UNINA9910974187103321
• Autore: Caldarelli Guido
• Pubbl/distr/stampa: Oxford, : Oxford University Press, 2007
• ISBN: 9780191526343; 0191526347
• Edizione: [1st ed.]
• Descrizione fisica: xiv, 309 p. : ill
• Collana: Oxford Finance Ser.
• Disciplina: 003
• Soggetti: System analysis; System theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Contents -- I: DEFINITIONS AND METHODOLOGY -- 1. Introduction to graphs -- 1.1 Graphs, directed graphs, and weighted graphs -- 1.2 Trees -- 1.3 Vertex correlation, assortativity -- 1.4 Hierarchical properties of graphs -- 1.5 The properties of scale-free networks -- 2. Graph structures: communities -- 2.1 Introduction -- 2.2 Typical subgraphs, motifs -- 2.3 Classes of vertices -- 2.4 Centrality measures, betweenness, and robustness -- 2.5 Clustering detection, modularity -- 2.6 Communities in graphs -- 3. Scale-invariance -- 3.1 Geometrical scale-invariance: fractals -- 3.2 Measuring the fractal dimension -- 3.3 Scale-invariance and power laws -- 3.4 Plotting a power law -- 3.5 Scale-invariance in natural sciences -- 3.6 Scale-invariance in economics and in social sciences -- 4. The origin of power-law functions -- 4.1 Random walk, Laplace equation, and fractals -- 4.2 Power laws from minimization principles -- 4.3 Multiplicative processes and normal distribution -- 4.4 Preferential attachment, the Matthew effect -- 5. Graph generating models -- 5.1 Random graph model -- 5.2 The small-world model -- 5.3 The Barabási-Albert model -- 5.4 Modifications to the Barabási-Albert model -- 5.5 Copying models -- 5.6 Fitness based model -- 5.7 Graph from optimization principles -- II: EXAMPLES -- 6. Networks in the cell -- 6.1 Basic cell biology -- 6.2 Protein-protein interaction network -- 6.3 Metabolic pathways -- 6.4 Gene regulatory networks -- ; 7. Geophysical networks -- 7.1 Satellite images and digital elevation models -- 7.2 Geometrical scale invariance for river networks -- 7.3 Scaling relations for river networks -- 7.4 River networks models -- 7.5 River networks on Mars' surface -- 8. Ecological networks -- 8.1 Species and evolution -- 8.2 Food webs: a very particular case of network -- 8.3 Food web quantities.; 8.4 Classifications of species -- 8.5 Yule process for taxonomies -- 9. Technological networks: Internet and WWW -- 9.1 The Internet protocols -- 9.2 The geography of the Internet -- 9.3 The autonomous systems -- 9.4 The scale-invariance in the Internet -- 9.5 The World Wide Web -- 9.6 Searching the web -- 9.7 Statistical measures of the Web -- 9.8 E-mail networks -- 10. Social and cognitive networks -- 10.1 Networks of scientific papers -- 10.2 Contact networks -- 10.3 Linguistic networks -- 10.4 Wikipedia -- 11. Financial networks -- 11.1 Board of directors -- 11.2 Stock networks -- 11.3 Bank networks -- 11.4 The world trade web -- III: APPENDICES -- A. Glossary -- A -- B -- C -- D -- E -- F -- G -- H -- I -- L -- M -- N -- O -- P -- R -- S -- T -- V -- W -- B. Graph quantities -- B.1 Basics -- B.2 Different kinds of graphs -- B.3 Paths, cycles, and trees -- C. Basic statistics -- C.1 Events and probability -- C.2 Probability densities and distributions -- C.3 Working with statistical distributions -- C.4 Statistical properties of weighted networks -- D. Matrices and eigenvectors -- E. Population dynamics -- E.1 Population dynamics -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- R -- S -- T -- V -- W -- Y -- Z.
• Sommario/riassunto: Many different systems both in nature and in technology can be described by means of networks of interconnected components. Despite their different aspects, all of them share similar mathematical properties. In this book we explain how to recognize these features and why these different systems develop this common structure.