1. Abstract Networks

7. WWW (2000)

9. Scientific Collaboration Girvan & Newman (2002)

11. Sexual Contact Potterat et al. (2002)

13. Community Structure Moody (2001)

15. SocialFriendships Business Relationships Sexual relationships Small World Networks InformationWWW citation Thesaurus TechnologicalInternet Power Grid Train, Plane, Road, River Routes BiologicalNeural Network Metabolic Protein Interactions Circulatory System

17. Some Questions to ask About Networks Technological Networks (eg Internet) Information Networks (eg WWW) Social Networks

19. Random N = 20 Av-k = 5

21. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

23. Bell-Shaped Distribution

25. Barabasi’s Results

27. Twitter

31. Power-Law Distribution

35. P(k) prob that node is connected to k other nodes Web Log-log

41. Scale Free Dia = 4

43. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

45. How are Scale-Free Networks Built?

47. Applications of Abstract Scale-Free Thinking

49. Diameter of the Web Albert, Jeong & Barabasi (1999) Nature. Definition 1 (Barabasi) “average of the shortest paths between all nodes. Definition 2 The longest of all shortest nodes.

51. Scale Free Dia = 4

53. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

55. Scale Free Dia = 4

57. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

59. Random Attack Nodes 1,12,18

61. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

63. Targeted Attack Nodes 4,5,6

65. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

67. Random N = 20 Av-k = 5

69. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

71. Random Attack Nodes 1,2,18

73. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

75. Targeted Attack Nodes 1,2,18

77. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

79. Network Resilience

81. Small Worlds – Social Networks N people in the world with z acquaintances. How many links l needed to get from and person to any other person?