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2011   11   7
•                (26)

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                    •   2010

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                    •   2011 7

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2011   11   7
Adgenda


                •              ?

                •   mixi

                •


2011   11   7
Adgenda


                •
                •   mixi

                •


2011   11   7
•   Web

                •   2007        Brad Fitzpatrick

                •   2007   F8     Mark Eliot Zuckerberg




                            http://bradfitz.com/social-graph-problem/

2011   11   7
•   Web

                •   2007        Brad Fitzpatrick

                •   2007   F8     Mark Eliot Zuckerberg




                            http://bradfitz.com/social-graph-problem/

2011   11   7
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                      mixi
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2011   11   7
Adgenda

                •                  ?

                •   mixi

                    •   mixi

                    •
                    •
                    •
                •
2011   11   7
mixi




                             ThinkSocial(2011   8   )
                  http://pr.mixi.co.jp/2011/08/15/mixiinfographic0815.html

2011   11   7
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2011   11   7
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2011   11   7
something post
                I’m runnning, now!




2011   11   7
something post
                I’m runnning, now!




2011   11   7
something post
                I’m runnning, now!




                                Feed Back




2011   11   7
something post
                I’m runnning, now!




                                Feed Back




2011   11   7
2011   11   7
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•


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•
       •

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R

                •
                •
                    •
                    •


                        http://www.r-project.org/




2011   11   7
Gephi
                •
                •   Google Summer Of Code



                •
                •
                                       http://gephi.org/



2011   11   7
Adgenda

                •                           ?

                •   mixi

                •
                    •
                    •
                    •   Girven-Newman

                    •   Gephi   R

2011   11   7
•
                •
                •




2011   11   7
•
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•
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2011   11   7
•
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                •   Q




2011   11   7
•
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2011   11   7
•
                •
                •
                            2
                    1               1
                                4
                        2
                                    1
                                2

2011   11   7
•
                    •
                •               1
                        B




                    A       D




                        C
2011   11   7
•
                    •
                •                   1
                        B
                                A
                                        3




                    A       D




                        C
2011   11   7
•
                    •
                •                             1
                        B
                                          A
                                                  3

                                (A,B,C)




                    A       D




                        C
2011   11   7
•
                    •
                •                             1
                        B
                                          A
                                                        3

                                (A,B,C)       (A,B,D)




                    A       D




                        C
2011   11   7
•
                    •
                •                             1
                        B
                                          A
                                                        3

                                (A,B,C)       (A,B,D)       (A,C,D)




                    A       D




                        C
2011   11   7
•
                    •
                •                             1
                        B
                                          A
                                                        3

                                (A,B,C)       (A,B,D)       (A,C,D)

                                                                      1
                                              (A,B,C)
                    A       D




                        C
2011   11   7
•
                    •
                •                             1
                        B
                                          A
                                                        3

                                (A,B,C)       (A,B,D)       (A,C,D)

                                                                      1
                                              (A,B,C)
                    A       D


                                                            = 1/3 = 0.33
                        C
2011   11   7
•
                    •




                        :               v

                        :   s, t

                        :   s,t
                              (    )v

2011   11   7
•

                •
            •       ≠

2011   11   7
•

                •
            •       ≠

2011   11   7
Q
                •
                    •




                        :

                        :(          i   )/(       )

                        :(      i                     )/
                            (       )

2011   11   7
2011   11   7
•     1hop


                         •                    40            40

                         •                         : 0.25

                         •     Girvan-Newman




                ThinkSocial(2011   8   )
http://pr.mixi.co.jp/2011/08/15/mixiinfographic0815.html         http://alpha.mixi.co.jp/blog/?p=144
2011   11   7
Girvan-Newman
            1.

            2.                       (betweenness score)

            3. betweenness score

            4.
                 betweenness score

            5.           2,3,4



2011   11   7
Gephi




                            41
                        (        +   40   )

                            236



2011   11   7
41
                (        +   40   )

                    236


2011   11   7
R
                #   igraph
                library(igraph)


                # Girven-Newman
                #            g
                eb <- edge.betweenness.community(g)

                #                                Q
                step <- 1:40
                for (i in step) {
                  memb <- community.to.membership(g, eb$merges, steps=i-1)
                  Q[i] <- modularity(g, memb$membership)
                }

                #                Q
                plot(step, Q, type=b)
2011   11   7
step   Q




2011   11   7
step     Q



                38   Q




2011   11   7
step             Q


                #       38
                > community.to.membership(g, eb$merges, steps=38)$csize
                [1] 26 11 4




2011   11   7
41
                (         +   40   )

                    236
                              3


2011   11   7
•

                •

                •

2011   11   7
(2hop)




2011   11   7
(2hop)




                    2598
                    3456

                           33
                                346




2011   11   7
Girven-Newman




                            ,
                   betweenness score




2011   11   7
Girven-Newman


                   # Girven-Newman
                   #                    1hop   2hop

                   # 1hop
                   > system.time(GirvenNewman(graph.1hop))

                       0.10    0.00    0.09


                   # 2hop
                   > system.time(GirvenNewman(graph.2hop))

                       77.61   0.02   78.99


2011   11   7
Girven-Newman


                   # Girven-Newman
                   #                    1hop   2hop

                   # 1hop
                   > system.time(GirvenNewman(graph.1hop))

                       0.10    0.00    0.09


                   # 2hop
                   > system.time(GirvenNewman(graph.2hop))

                       77.61   0.02   78.99


2011   11   7
Girven-Newman


                   # Girven-Newman
                   #                    1hop   2hop

                   # 1hop
                   > system.time(GirvenNewman(graph.1hop))

                       0.10    0.00    0.09


                   # 2hop
                   > system.time(GirvenNewman(graph.2hop))

                       77.61   0.02   78.99


2011   11   7
•   "Fast algorithm for detecting community structure in
                networks"
                •   M.E.J.Newman

                •   Phys. Rev. E 69, 066133(2004)



            •   Newman

                •
                •                                   ΔQ

                •
            •
2011   11   7
#                    1hop   2hop
                # 1hop
                > system.time(GirvenNewman(graph.1hop))

                    0.10    0.00    0.09

                > system.time(Newman(graph.1hop))

                    0.08    0.00    0.04

                # 2hop
                > system.time(GirvenNewman(graph.2hop))

                    77.61   0.02   78.99

                > system.time(Newman(graph.2hop))

                    25.49   0.02   26.35
2011   11   7
#                    1hop   2hop
                # 1hop
                > system.time(GirvenNewman(graph.1hop))

                    0.10    0.00    0.09

                > system.time(Newman(graph.1hop))

                    0.08    0.00    0.04

                # 2hop
                > system.time(GirvenNewman(graph.2hop))

                    77.61   0.02   78.99

                > system.time(Newman(graph.2hop))

                    25.49   0.02   26.35
2011   11   7
#                    1hop   2hop
                # 1hop
                > system.time(GirvenNewman(graph.1hop))

                    0.10    0.00    0.09

                > system.time(Newman(graph.1hop))

                    0.08    0.00    0.04

                # 2hop
                > system.time(GirvenNewman(graph.2hop))

                    77.61   0.02   78.99

                > system.time(Newman(graph.2hop))

                    25.49   0.02   26.35
2011   11   7
#                    1hop   2hop
                # 1hop
                > system.time(GirvenNewman(graph.1hop))

                    0.10    0.00    0.09

                > system.time(Newman(graph.1hop))

                    0.08    0.00    0.04

                # 2hop
                > system.time(GirvenNewman(graph.2hop))

                    77.61   0.02   78.99

                > system.time(Newman(graph.2hop))

                    25.49   0.02   26.35
2011   11   7
(1)
                •   "Finding community structure in very large
                    networks"
                    •   Aaron Clauset, M.E.J.Newman, Cristopher Moore

                    •   Phys. Rev. E 70, 066111(2004)




                •   Newman

                    •                             ΔQ

                    •
2011   11   7
(2)
                •   "Fast unfolding of communities in large
                    networks"
                    •   Vincent D.Blondel, Jean-Loup Guilaume, Renaud Lambiotte, Etienne Lefebvre

                    •   J. Stat. Mech. (2008) P10008




                •   ΔQ

                •   CPU : bi-opteron 2.2G, memory 24G
                    •     1   2000             152min


2011   11   7
•
                    •   mixi

                    •
                    •
                •

                    •
                    •   Girven-Newman

                    •
2011   11   7
"Finding and evaluating community structure in networks"
                M.E.J.Newman and M.Girvan
                Phys. Rev. E 69, 026113(2004)

                "Fast algorithm for detecting community structure in networks"
                M.E.J.Newman
                Phys. Rev. E 69, 066133(2004)

                "Finding community structure in very large networks"
                Aaron Clauset, M.E.J.Newman, Cristopher Moore
                Phys. Rev. E 70, 066111(2004)

                "Fast unfolding of communities in large networks"
                Vincent D.Blondel, Jean-Loup Guilaume, Renaud Lambiotte, Etienne
                Lefebvre
                J. Stat. Mech. (2008) P10008




2011   11   7

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WebDBforum2011

  • 1. mixi 2011 11 7
  • 2. (26) • • 2010 • • 2011 7 • • • ( ) 2011 11 7
  • 3. Adgenda • ? • mixi • 2011 11 7
  • 4. Adgenda • • mixi • 2011 11 7
  • 5. Web • 2007 Brad Fitzpatrick • 2007 F8 Mark Eliot Zuckerberg http://bradfitz.com/social-graph-problem/ 2011 11 7
  • 6. Web • 2007 Brad Fitzpatrick • 2007 F8 Mark Eliot Zuckerberg http://bradfitz.com/social-graph-problem/ 2011 11 7
  • 7. 2011 11 7
  • 8. Vertex (node : ) 2011 11 7
  • 9. Vertex (node : ) Edge ( ) 2011 11 7
  • 10. Vertex (node : ) Undirected graph ( ) Edge ( ) 2011 11 7
  • 11. Vertex (node : ) 2011 11 7
  • 12. Vertex (node : ) Edge ( ) 2011 11 7
  • 13. Vertex (node : ) Directed graph ( ) Edge ( ) 2011 11 7
  • 14. Undirected graph ( ) 2011 11 7
  • 15. Vertex ( ) Undirected graph ( ) 2011 11 7
  • 16. Vertex ( ) Undirected graph ( ) Edge ( ) 2011 11 7
  • 17. Vertex ( ) Undirected graph ( ) Edge ( ) ( ) mixi 2011 11 7
  • 18. Vertex ( ) Directed graph ( ) Edge ( ) 2011 11 7
  • 19. Vertex ( ) Directed graph ( ) Edge ( ) ( ) Twitter follow 2011 11 7
  • 20. Adgenda • ? • mixi • mixi • • • • 2011 11 7
  • 21. mixi ThinkSocial(2011 8 ) http://pr.mixi.co.jp/2011/08/15/mixiinfographic0815.html 2011 11 7
  • 22. 2011 11 7
  • 23. 2011 11 7
  • 24. 2011 11 7
  • 25. 2011 11 7
  • 26. 2011 11 7
  • 27. 2011 11 7
  • 28. something post I’m runnning, now! 2011 11 7
  • 29. something post I’m runnning, now! 2011 11 7
  • 30. something post I’m runnning, now! Feed Back 2011 11 7
  • 31. something post I’m runnning, now! Feed Back 2011 11 7
  • 32. 2011 11 7
  • 33. 2011 11 7
  • 34. • 2011 11 7
  • 35. • 2011 11 7
  • 36. 2011 11 7
  • 37. 2011 11 7
  • 38. R • • • • http://www.r-project.org/ 2011 11 7
  • 39. Gephi • • Google Summer Of Code • • http://gephi.org/ 2011 11 7
  • 40. Adgenda • ? • mixi • • • • Girven-Newman • Gephi R 2011 11 7
  • 41. • • 2011 11 7
  • 42. • • 2011 11 7
  • 43. • • 2011 11 7
  • 44. • • • Q 2011 11 7
  • 45. • • 2011 11 7
  • 46. • • 2 1 1 4 2 1 2 2011 11 7
  • 47. • • 1 B A D C 2011 11 7
  • 48. • • 1 B A 3 A D C 2011 11 7
  • 49. • • 1 B A 3 (A,B,C) A D C 2011 11 7
  • 50. • • 1 B A 3 (A,B,C) (A,B,D) A D C 2011 11 7
  • 51. • • 1 B A 3 (A,B,C) (A,B,D) (A,C,D) A D C 2011 11 7
  • 52. • • 1 B A 3 (A,B,C) (A,B,D) (A,C,D) 1 (A,B,C) A D C 2011 11 7
  • 53. • • 1 B A 3 (A,B,C) (A,B,D) (A,C,D) 1 (A,B,C) A D = 1/3 = 0.33 C 2011 11 7
  • 54. • : v : s, t : s,t ( )v 2011 11 7
  • 55. • • ≠ 2011 11 7
  • 56. • • ≠ 2011 11 7
  • 57. Q • • : :( i )/( ) :( i )/ ( ) 2011 11 7
  • 58. 2011 11 7
  • 59. 1hop • 40 40 • : 0.25 • Girvan-Newman ThinkSocial(2011 8 ) http://pr.mixi.co.jp/2011/08/15/mixiinfographic0815.html http://alpha.mixi.co.jp/blog/?p=144 2011 11 7
  • 60. Girvan-Newman 1. 2. (betweenness score) 3. betweenness score 4. betweenness score 5. 2,3,4 2011 11 7
  • 61. Gephi 41 ( + 40 ) 236 2011 11 7
  • 62. 41 ( + 40 ) 236 2011 11 7
  • 63. R # igraph library(igraph) # Girven-Newman # g eb <- edge.betweenness.community(g) # Q step <- 1:40 for (i in step) { memb <- community.to.membership(g, eb$merges, steps=i-1) Q[i] <- modularity(g, memb$membership) } # Q plot(step, Q, type=b) 2011 11 7
  • 64. step Q 2011 11 7
  • 65. step Q 38 Q 2011 11 7
  • 66. step Q # 38 > community.to.membership(g, eb$merges, steps=38)$csize [1] 26 11 4 2011 11 7
  • 67. 41 ( + 40 ) 236 3 2011 11 7
  • 68. • • 2011 11 7
  • 69. (2hop) 2011 11 7
  • 70. (2hop) 2598 3456 33 346 2011 11 7
  • 71. Girven-Newman , betweenness score 2011 11 7
  • 72. Girven-Newman # Girven-Newman # 1hop 2hop # 1hop > system.time(GirvenNewman(graph.1hop)) 0.10 0.00 0.09 # 2hop > system.time(GirvenNewman(graph.2hop)) 77.61 0.02 78.99 2011 11 7
  • 73. Girven-Newman # Girven-Newman # 1hop 2hop # 1hop > system.time(GirvenNewman(graph.1hop)) 0.10 0.00 0.09 # 2hop > system.time(GirvenNewman(graph.2hop)) 77.61 0.02 78.99 2011 11 7
  • 74. Girven-Newman # Girven-Newman # 1hop 2hop # 1hop > system.time(GirvenNewman(graph.1hop)) 0.10 0.00 0.09 # 2hop > system.time(GirvenNewman(graph.2hop)) 77.61 0.02 78.99 2011 11 7
  • 75. "Fast algorithm for detecting community structure in networks" • M.E.J.Newman • Phys. Rev. E 69, 066133(2004) • Newman • • ΔQ • • 2011 11 7
  • 76. # 1hop 2hop # 1hop > system.time(GirvenNewman(graph.1hop)) 0.10 0.00 0.09 > system.time(Newman(graph.1hop)) 0.08 0.00 0.04 # 2hop > system.time(GirvenNewman(graph.2hop)) 77.61 0.02 78.99 > system.time(Newman(graph.2hop)) 25.49 0.02 26.35 2011 11 7
  • 77. # 1hop 2hop # 1hop > system.time(GirvenNewman(graph.1hop)) 0.10 0.00 0.09 > system.time(Newman(graph.1hop)) 0.08 0.00 0.04 # 2hop > system.time(GirvenNewman(graph.2hop)) 77.61 0.02 78.99 > system.time(Newman(graph.2hop)) 25.49 0.02 26.35 2011 11 7
  • 78. # 1hop 2hop # 1hop > system.time(GirvenNewman(graph.1hop)) 0.10 0.00 0.09 > system.time(Newman(graph.1hop)) 0.08 0.00 0.04 # 2hop > system.time(GirvenNewman(graph.2hop)) 77.61 0.02 78.99 > system.time(Newman(graph.2hop)) 25.49 0.02 26.35 2011 11 7
  • 79. # 1hop 2hop # 1hop > system.time(GirvenNewman(graph.1hop)) 0.10 0.00 0.09 > system.time(Newman(graph.1hop)) 0.08 0.00 0.04 # 2hop > system.time(GirvenNewman(graph.2hop)) 77.61 0.02 78.99 > system.time(Newman(graph.2hop)) 25.49 0.02 26.35 2011 11 7
  • 80. (1) • "Finding community structure in very large networks" • Aaron Clauset, M.E.J.Newman, Cristopher Moore • Phys. Rev. E 70, 066111(2004) • Newman • ΔQ • 2011 11 7
  • 81. (2) • "Fast unfolding of communities in large networks" • Vincent D.Blondel, Jean-Loup Guilaume, Renaud Lambiotte, Etienne Lefebvre • J. Stat. Mech. (2008) P10008 • ΔQ • CPU : bi-opteron 2.2G, memory 24G • 1 2000 152min 2011 11 7
  • 82. • mixi • • • • • Girven-Newman • 2011 11 7
  • 83. "Finding and evaluating community structure in networks" M.E.J.Newman and M.Girvan Phys. Rev. E 69, 026113(2004) "Fast algorithm for detecting community structure in networks" M.E.J.Newman Phys. Rev. E 69, 066133(2004) "Finding community structure in very large networks" Aaron Clauset, M.E.J.Newman, Cristopher Moore Phys. Rev. E 70, 066111(2004) "Fast unfolding of communities in large networks" Vincent D.Blondel, Jean-Loup Guilaume, Renaud Lambiotte, Etienne Lefebvre J. Stat. Mech. (2008) P10008 2011 11 7