Random graphs with arbitrary degree distributions and their applications

Chapters in this book

1. Frontmatter i
2. Contents v
3. Preface ix
4. Chapter One. Introduction 1
5. Chapter Two. Historical developments
6. Chain-links 21
7. Connectivity of random nets 27
8. On the evolution of random graphs 38
9. Contacts and influence 83
10. An experimental study of the small world problem 130
11. Networks of scientific papers 149
12. Famous trails to Paul Erdös 155
13. Chapter 3. Empirical Studies
14. Diameter of the world-wide web 182
15. Graph structure in the web 183
16. On power-law relationships of the internet topology 195
17. Classes of small-world networks 207
18. The large-scale organization of metabolic networks 211
19. The small world of metabolism 215
20. Network Motifs: Simple Building Blocks of Complex Networks 217
21. The structure of scientific collaboration networks 221
22. The web of human sexual contacts 227
23. Chapter 4. Models of networks
24. 4.1 RANDOM GRAPH MODELS 229
25. A Critical Point for Random Graphs with a Given Degree Sequence 240
26. A Random Graph Model for Massive Graphs 259
27. Random graphs with arbitrary degree distributions and their applications 269
28. 4.2 THE SMALL-WORLD MODEL 286
29. Collective dynamics of 'small-world' networks 301
30. Small-World Networks: Evidence for a Crossover Picture 304
31. Comment on "Small-world networks: Evidence for crossover picture" 308
32. Scaling and percolation in the small-world network model 310
33. On the properties of small-world network models 321
34. 4.3 MODELS OF SCALE-FREE NETWORKS 335
35. Emergence of Scaling in Random Networks 349
36. Structure of Growing Networks with Preferential Linking 353
37. Connectivity of Growing Ra ndom Networks 357
38. Competition and multiscaling m evolving networks 361
39. Universal Behavior of Load Distribution in Scale-Free Networks 368
40. Spectra of "real-world" graphs: Beyond the semicircle law 372
41. The Degree Sequence of a Scale-Free Random Graph Process 384
42. A MODEL OF LARGE-SCALE PROTEOME EVOLUTION 396
43. Modeling of Protein Interaction Networks 408
44. Chapter Five. Applications
45. 5.1 EPIDEMICS AND RUMORS 415
46. 5.2 ROBUSTNESS OF NETWORKS 424
47. 5.3 SEARCHING NETWORKS 428
48. EPIDEMICS WITH TWO LEVELS OF MIXING 436
49. The effects of local spatial structure on epidemiological invasions 480
50. Small World Effect in an Epidemiological Model 489
51. Epidemic Spreading in Scale-Free Networks 493
52. A simple model of global cascades on random networks 497
53. Error and attack tolerance of complex networks 503
54. Resilience of the Internet to Random Breakdowns 507
55. Network Robustness and Fragility: Percolation on Random Graphs 510
56. Authoritative Sources in a Hyperlinked Environment 514
57. Search in power-law networks 543
58. Navigation in a small world 551
59. Chapter Six. Outlook 553
60. References 559
61. Index 575