More Related Content Similar to WebDBforum2011 Similar to WebDBforum2011 (9) 2. • (26)
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• 2010
•
• 2011 7
•
•
• ( )
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
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
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
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
57. Q
•
•
:
:( i )/( )
:( i )/
( )
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
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
70. (2hop)
2598
3456
33
346
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
