1. The Page Rank Axioms Based on Ranking Systems: The PageRank Axioms , by Alon Altman and Moshe Tennenholtz. Presented by Aron Matskin

28. DEL: Proof a c b d c b d a VBC

29. DEL: Proof c b d a VBC c b d a

30. DEL: Proof ISO,PRO c b d a c b d a

31. DEL: Proof PRO c d a c b d a

32. DEL: Proof PRO c d a c d a

33. DEL: Proof VBC c d a c d a

34. DEL: Proof VBC c d a a c d

37. DELETE: Proof x = = = = COL x y

38. DELETE: Proof PRO x y

40. DUPLICATE: Proof c b d a c b d a VBC

41. DUPLICATE: Proof c b d a VBC c b d a

42. DUPLICATE: Proof c b d a COL c b d a

43. DUPLICATE: Proof c b d a ISO,PRO c b d a

44. DUPLICATE: Proof c b d a COL -1 c b d a

45. DUPLICATE: Proof VBC -1 c b d a c b d a

47. Proof by Example on b and d b c a a b c a b c G A G d d d R G a b c d 0 1 1 0 0 0 0 ⅓ ½ 0 0 ⅓ ½ 0 0 ⅓ 4 1 3 3

49. Step 2: Choose Node to Remove b c a d

50. Step 3: Remove “self-edges” b c a d

51. Step 4: Duplicate Predecessors b c a d

52. Step 5: DELETE the Node b c d

55. Step 5: DELETE the Node b d

58. Step 8: Equalize by Reverse DEL b d By ISO b=d. By DEL and SE: in G’ b<d.

59. Example for a and d b c a d b c a d

60. After Removal of c b a d

61. Duplicate Predecessors of b b a d

62. DELETE b a d

63. DELETE Extras a d

64. Before Balancing a d

65. After Balancing a d Conclusion: a<d.

66. What about a and b ? b a d

67. What about a and b ? b a d

68. What about a and b ? b a

69. What about a and b ? b a

70. What about a and b ? b a

71. What about a and b ? b a Conclusion: a=b.

73. The End c b d a ½ 0 0 ½ 0 1 0 1 0 a b c a b c