LEADER 05388nam 2200673Ia 450 001 9910145913003321 005 20170814180846.0 010 $a1-280-52099-X 010 $a9786610520992 010 $a3-527-60633-5 010 $a3-527-60275-5 035 $a(CKB)1000000000016780 035 $a(EBL)481793 035 $a(OCoLC)69176514 035 $a(SSID)ssj0000167634 035 $a(PQKBManifestationID)11171509 035 $a(PQKBTitleCode)TC0000167634 035 $a(PQKBWorkID)10178995 035 $a(PQKB)11469897 035 $a(MiAaPQ)EBC481793 035 $a(EXLCZ)991000000000016780 100 $a20021223d2003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aHandbook of graphs and networks$b[electronic resource] $efrom the Genome to the Internet /$fStefan Bornholdt, Heinz Georg Schuster (eds.) 205 $a1st ed. 210 $aWeinheim ;$a[Cambridge] $cWiley-VCH$dc2003 215 $a1 online resource (419 p.) 300 $aDescription based upon print version of record. 311 $a3-527-40336-1 320 $aIncludes bibliographical references and index. 327 $aHandbook 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 Baraba?si-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 327 $a1.13 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 327 $a2.6 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 327 $a4.1.1 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 327 $a5 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 Baraba?si-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 327 $a6.2 Nematode developmental biology: studying processes at a cellular level 330 $aComplex 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 606 $aSystem analysis 606 $aGraph theory 606 $aCombinatorial analysis 608 $aElectronic books. 615 0$aSystem analysis. 615 0$aGraph theory. 615 0$aCombinatorial analysis. 676 $a003 676 $a511.5 701 $aBornholdt$b Stefan$0737704 701 $aSchuster$b Heinz Georg$f1943-$048625 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910145913003321 996 $aHandbook of graphs and networks$91460732 997 $aUNINA