Handbook of graphs and networks [[electronic resource] ] : from the Genome to the Internet / / Stefan Bornholdt, Heinz Georg Schuster (eds.)

• Pubblicazione: Weinheim ; ; [Cambridge], : Wiley-VCH, c2003
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (419 p.)
• Disciplina: 003; 511.5
• Soggetto topico: System analysis; Graph theory; Combinatorial analysis
• Altri autori: BornholdtStefan SchusterHeinz Georg <1943->
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Handbook of Graphs and Networks From the Genome to the Internet; Preface; Contents; List of contributors; 1 Mathematical results on scale-free random graphs; 1.1 Introduction; 1.2 Classical models of random graphs; 1.3 Results for classical random graphs; 1.4 The Watts-Strogatz 'small-world' model; 1.5 Scale-free models; 1.6 The Barabási-Albert model; 1.7 The LCD model and G((n))(m); 1.8 The Buckley-Osthus model; 1.9 The copying model; 1.10 The Cooper-Frieze model; 1.11 Directed scale-free graphs; 1.12 Clustering coefficient and small subgraphs ; 1.13 Pairings on [0, 1] and the diameter of the LCD model1.14 Robustness and vulnerability; 1.15 The case [0, 1]: plane-oriented recursive trees; 1.16 Conclusion; References; 2 Random graphs as models of networks; 2.1 Introduction; 2.2 Random graphs with specified degree distributions; 2.3 Probability generating functions; 2.3.1 Properties of generating functions; 2.3.2 Examples; 2.4 Properties of undirected graphs; 2.4.1 Distribution of component sizes; 2.4.2 Mean component size; 2.4.3 Above the phase transition; 2.5 Properties of directed graphs; 2.5.1 Generating functions; 2.5.2 Results ; 2.6 Networks with clustering2.7 Models defined on random graphs; 2.7.1 Network resilience; 2.7.2 Epidemiology; 2.7.3 The SIR model; 2.7.4 Solution of the SIR model; 2.8 Summary; References; 3 Emergence of scaling in complex networks; 3.1 Introduction; 3.2 Network models; 3.2.1 Random networks; 3.2.2 Scale-free networks; 3.2.3 Scale-free model; 3.3 Fitness model and Bose-Einstein condensation; 3.4 The Achilles' Heel of complex networks; 3.5 A deterministic scale-free model; 3.6 Outlook; 3.7 Acknowledgments; References; 4 Structural properties of scale-free networks; 4.1 Introduction ; 4.1.1 Random graphs4.1.2 Scale-free networks; 4.2 Small and Ultra-small worlds; 4.2.1 Diameter of scale-free networks; 4.2.2 Minimal graphs and lower bound; 4.2.3 The general case of random scale-free networks; 4.3 Percolation; 4.3.1 Random breakdown; 4.3.2 Percolation critical threshold; 4.3.3 Generating functions; 4.3.4 Intentional attack; 4.3.5 Critical exponents; 4.3.6 Fractal dimension; 4.4 Percolation in directed networks; 4.4.1 Threshold; 4.4.2 Critical exponents; 4.5 Efficient immunization strategies; 4.5.1 Acquaintance immunization; 4.6 Summary and outlook; References ; 5 Epidemics and immunization in scale-free networks5.1 Introduction; 5.2 Computers and epidemiology; 5.3 Epidemic spreading in homogeneous networks; 5.4 Real data analysis; 5.5 Epidemic spreading in scale-free networks; 5.5.1 Analytic solution for the Barabási-Albert network; 5.5.2 Finite size scale-free networks; 5.6 Immunization of scale-free networks; 5.6.1 Uniform immunization; 5.6.2 Targeted immunization; 5.7 Conclusions; References; 6 Cells and genes as networks in nematode development and evolution; 6.1 Introduction ; 6.2 Nematode developmental biology: studying processes at a cellular level
• Sommario/riassunto: Complex interacting networks are observed in systems from such diverse areas as physics, biology, economics, ecology, and computer science. For example, economic or social interactions often organize themselves in complex network structures. Similar phenomena are observed in traffic flow and in communication networks as the internet. In current problems of the Biosciences, prominent examples are protein networks in the living cell, as well as molecular networks in the genome. On larger scales one finds networks of cells as in neural networks, up to the scale of organisms in ecological food web
• Titolo autorizzato: Handbook of graphs and networks
• ISBN: 1-280-52099-X; 9786610520992; 3-527-60633-5; 3-527-60275-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910830019403321
• Lo trovi qui: Univ. Federico II