1 2 : etc = x(t + 1) = 1 ax(t) 2 + y(t) y(t + 1) = bx(t) x y 2006 p.2/58
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1 Tel : , Fax : tohru@ics.saitama-u.ac.jp URL : tohru 2006 p.1/58
2 1 2 : etc = x(t + 1) = 1 ax(t) 2 + y(t) y(t + 1) = bx(t) x y 2006 p.2/58
3 ( ) x 4 x 7 x 3 x 5 x 8 x 6 x 2 x p.3/58
4 1.? p.4/58
5 [ ] World Wide Web [ ] ( SARS) ( / ) 2006 p.5/58
6 2006 p.6/58
7 Stanley Milgram ( ) Witchita (Kansas ) Boston (Massachusetts ) Omaha(Nebraska ) Boston (Massachusetts ) 2006 p.7/58
8 2006 p.8/58
9 2006 p.9/58
10 ? 2006 p.10/58
11 S. Milgram: The Small-World Problem, Psychology Today, Vol.1, pp.67 67, p.11/58
12 : The Oracle says: Harrison Ford has a Bacon number of. Harrison Ford was in Clear and Present Danger (1994) with John Lafayette. John Lafayette was in Loverboy (2005) with Kevin Bacon p.12/58
13 ,975 1, , , , , , , , , , , , ,732 ( ) 2006 p.13/58
14 [ ] World Wide Web [ ] ( SARS) ( / ) 2006 p.14/58
15 ? 6 ( ) WWW ( ) ( ) OK 2006 p.15/58
16 2006 p.16/58
17 (1736 ) Euler, Cauchy, Hamilton, Cayley, Kirchhoff... Erdös, Rényi (random network, 1950 s) (1998 ) Watts and Strogatz (small world network, 1998) Barabási and colleagues (scale free network, 1999) (graph) 2006 p.17/58
18 (1736) ( ) (1875 ) c d g e a b f 2006 p.18/58
19 Euler (1736) c d g e a b f 2006 p.19/58
20 C A D B 2006 p.20/58
21 Euler (1736) ( ) 2006 p.21/58
22 1875 C c d g A e D a b f B 2006 p.22/58
23 c C d g A e D a b f B 2006 p.23/58
24 p.24/58
25 p.25/58
26 2006 p.26/58
27 2006 p.27/58
28 (20 ) 2006 p.28/58
29 (the number of vertices) N (degree) k i (i = 1, 2,..., N) v i = v i (degree distribution) p(k) (degree) < k >= kp(k) k=0 (avarege path length) L (clustering coefficients) C ( ) 2006 p.29/58
30 v i v i v i v i C i C 2006 p.30/58
31 p.31/58
32 ? 2006 p.32/58
33 Random Rewiring (Watts and Strogatz, 1998) p = 0 p = 1 p random rewiring 2006 p.33/58
34 Random Rewiring L,C C(p)/C(0) L(p)/L(0) p 2006 p.34/58
35 L C L L R L/L R C C R C/C R p.35/58
36 P(k) k γ ( ) ( ) 2006 p.37/58
37 2006 p.38/58
38 2006 p.39/58
39 2006 p.40/58
40 2006 p.41/58
41 2006 p.42/58
42 2006 p.43/58
43 2006 p.44/58
44 p(k) ( ) p(k) k γ k ( ) 2006 p.45/58
45 WWW Yahoo Google 2006 p.46/58
46 1. m 0 2. m(< m 0 ) 3. v i k i v i Π(k i ) = k i, (1 i n) n k i i= p.47/58
47 t = 0 t = 1 t = 2 t = 3 t = 4 t = p.48/58
48 p(k i ) p(k i ) k i p(k) k k i 2006 p.49/58
49 = etc 2006 p.50/58
50 ? ( )? 2006 p.51/58
51 : NHK p.52/58
52 : p.53/58
53 : SYNC p.54/58
54 Duncan J. Watts, Six Degrees, The Science of a Connected Age, W. W. Norton & Company, p.55/58
55 Duncan J. Watts, Small Worlds, The Dynamics of Networks between Order and Randomness, Princeton University Press, 1999; : p.56/58
56 : 2005; : p.57/58
1. 1 H18 p.2/37
( ) 338 8570 255 Tel : 048 858 3577, Fax : 048 858 3716 Email : tohru@nls.ics.saitama-u.ac.jp URL : http://www.nls.ics.saitama-u.ac.jp/ tohru H18 p.1/37 1. 1 H18 p.2/37 1. 1 2. (a) H17 (b) 50 90 H18 p.2/37
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