05388nam 2200673Ia 450 991014591300332120170814180846.01-280-52099-X97866105209923-527-60633-53-527-60275-5(CKB)1000000000016780(EBL)481793(OCoLC)69176514(SSID)ssj0000167634(PQKBManifestationID)11171509(PQKBTitleCode)TC0000167634(PQKBWorkID)10178995(PQKB)11469897(MiAaPQ)EBC481793(EXLCZ)99100000000001678020021223d2003 uy 0engur|n|---|||||txtccrHandbook of graphs and networks[electronic resource] from the Genome to the Internet /Stefan Bornholdt, Heinz Georg Schuster (eds.)1st ed.Weinheim ;[Cambridge] Wiley-VCHc20031 online resource (419 p.)Description based upon print version of record.3-527-40336-1 Includes bibliographical references and index.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 subgraphs1.13 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 Results2.6 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 Introduction4.1.1 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; References5 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 Introduction6.2 Nematode developmental biology: studying processes at a cellular levelComplex 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 webSystem analysisGraph theoryCombinatorial analysisElectronic books.System analysis.Graph theory.Combinatorial analysis.003511.5Bornholdt Stefan737704Schuster Heinz Georg1943-48625MiAaPQMiAaPQMiAaPQBOOK9910145913003321Handbook of graphs and networks1460732UNINA