Analisi delle dinamiche di sopravvivenza e proliferazione delle keyword negli articoli scientifici
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(102) Size k out. in. l. real. 8.32. 7.61. 4.77. pow. 8.85. 5.2 7.67 7.47 4.01 1.95 3.86 6.53. l. 6.3 8.75 12.8 3.65 2.12 5.01 8.2. 2.89. rand. 3.32. 1.71 2. l. 2.26 3.23. Albert, Jeong, and Baraba´ si 1999 K umar et al., 1999 Broder et al., 2000 H uberman and A damic, 2000 Faloutsos, 1999 Faloutsos, 1999 Govindan, 2000 Baraba´ si and Albert, 1999 Newman, 2001b Baraba´ si et al., 2001 Baraba´ si et al., 2001 L ilj eros et al., 2001 Jeong et al., 2000 J eong, Mason, et al., 2001 Montoya and Sole´ , 2000 Montoya and Sole´ , 2000 R edner, 1998 A iello et al., 2000 Ferrer i C ancho and Sole´ , 2001 Yook et al., 2001b. Reference. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14 16 17 18 19 20. Nr.. TABLE II. The scaling exponents characterizing the degree distribution of several scale-free networks, for which P (k) follows a power law (2). We indicate the size of the network, its average degree k , and the cutoff for the power-law scaling. For directed networks we list separately the indegree ( in ) and outdegree ( out ) exponents, while for the undirected networks, marked with an asterisk (*), these values are identical. The columns l real , l rand , and l pow compare the average path lengths of real networks with power-law degree distribution and the predictions of random-graph theory (17) and of Newman, Strogatz, and Watts (2001) [also see Eq. (63) above], as discussed in Sec. V. The numbers in the last column are keyed to the symbols in Figs. 8 and 9. Network. WWW 325 729 4.51 900 2.45 2.1 11.2 WWW 7 2.38 2.1 4 107 WWW 7.5 4000 2.72 2.1 16 2 108 W W W, site 260 000 1.94 Internet, domain * 3015–4389 3.42–3.76 30–40 2.1–2.2 2.1–2.2 4 Internet, router * 3888 2.57 30 2.48 2.48 12.15 150 000 2.66 60 2.4 2.4 11 Internet, router * Movie actors * 212 250 28.78 900 2.3 2.3 4.54 Co-authors, SPIRES * 56 627 173 1100 1.2 1.2 4 209 293 11.54 400 2.1 2.1 6 Co-authors, neuro. * Co-authors, math. * 70 975 3.9 120 2.5 2.5 9.5 2810 3.4 3.4 Sexual contacts* Metabolic, E. coli 778 7.4 110 2.2 2.2 3.2 Protein, S. cerev.* 1870 2.39 2.4 2.4 Ythan estuary * 134 8.7 35 1.05 1.05 2.43 154 4.75 27 1.13 1.13 3.4 Silwood Park * C it a t io n 783 339 8.57 3 Phone call 3.16 2.1 2.1 53 106 Words, co-occurrence * 460 902 70.13 2.7 2.7 Words, synonyms* 22 311 13.48 2.8 2.8. $
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(289) . Q . * ( . . . P (k). . P (h ) P (k) = βk −γ β = 22, 4 ± 0, 7 γ P (hW ) C . 4 ( * . W. B
(290) ,, %
(291) & 0 D
(292) ,, %
(293)
(294) &. . . (. P (k)" P (hA ). . . A. h = 10. . A. P (h ). . 1 ≤ k ≤ 15". 4 . ;. * . . k=9. . P (k)1.
(295)
(296) . -
(297) . . 1993 1997 2001. . 5
(298) 3. 2001. Gt. GW t. ". t. . 19936 1997.
(299)
(300) . t '' '' ''K '' '') '' '''
(301) ,,,
(302) ,,. . -
(303) . α 0, 69 ± 0, 01 0, 68 ± 0, 01 0, 68 ± 0, 01 0, 68 ± 0, 01 0, 68 ± 0, 01 0, 68 ± 0, 01 0, 68 ± 0, 01 0, 67 ± 0, 01 0, 68 ± 0, 01. . γ 2, 36 ± 0, 01 2, 33 ± 0, 01 2, 33 ± 0, 01 2, 36 ± 0, 01 2, 34 ± 0, 01 2, 34 ± 0, 01 2, 31 ± 0, 01 2, 27 ± 0, 01 2, 31 ± 0, 01. 7 8" "& "% . P (hW ) . ( -. . ( ( . + . P (hA ). (. . . . K H P * " . -. k = 14. . . ( . . 9. . . . A. h = 15. . 10 . P (k) 1 ≤ hW ≤ 10. . w. h > 100. . 1 ≤ k ≤ 30. . " ( . k > 200. . $" 4 . ( ( ; . 5 . . : L BMD. %&" . . . . 4 . ( ;. . . C. . 7 8 - . . . . . . B . . ;. / . - . - . ½. . 4 . . P (hW = 1) ≈ 0, 68. " . " . . 68%. . C . (M . ½ !
(304)
(305)
(306) .
(307)
(308) .
(309) .
(310)
(311) . . . P (k)1. - ( . ) /. 1993. P (hW ). -
(312) . 6 . . . . . ". . GW t. . " . . . . *. . . . . k > 1000<. ? . . 1997. . . H . 2001. * 6. -. %K&" %
(313) '& %&" . - .
(314)
(315) . -
(316) . . .
(317) ( 4 . J. . - . 4 - . . . . 7. ( 2. =8" ( . 7 (. ¾. . 2 =8 - . . . . . / . . . * . 5 . * . W. a2. . . . . W a1 = W a2. B . . . . . (" . a1. kw ". . a2 ". . . ( . a2 *" W hW w = 1 hw = 21. . W a1 ⊃ W a2 . . . w . ;. W a1. . . C * (" . G ( . . . w. . . W a1 ∩ W a2 = {w} |W ai | = 1 i = 1, 2 C * kw " * . hW w = 1 C. . . .
(318) B . a1. * . . . hW w = 2. . . . . . 1; . . . .. - ( . * . Gt . . . / > * . * (" . kw. . w. 4 . . a1. P . . ¾ . |W. .
(319) . a2 ". 4 . A a1 kw = |W a1 | + |W a2 | − |W a1 ∩ W a2 | − 1 = hA ∩ W a2 | − 1. a1 + ha2 − |W. - +. . a1. a2. ∩ W |. . 5. . 78. 4 - * + . . . "
(320)
(321) . . #. . 4. . .
(322)
(323) Caso 1. -
(324) . . Caso 2 a2. a1. a1. a2. w. w. w. w. . .
(325) " . w 9 , " (" a2 . " W 1 7
(326)
(327) hw = 2 kw kw = 8. . n 7hW w = n8. = 4: 7
(328)
(329) hW w =2. - - * ( . . + . n. . 3 . ( 4 G . * . . .. w1. * . w1 w2 hWw w2 . 1. = hW w2. kw. 1. > kw 2 . 4 ? . . H ? . hW. . k. . . * . . . G * . (M . -. . . . / K * ( . hW. . k. . . . * . ''K .
(330) ,,. *
(331) ,, *. * 4 - . k = a(hW − b)c ,. 7
(332) 8.
(333)
(334) . *. a = 14, 3 ± 0, 6" b = 0, 43 ± 0, 06. * . . Q . . -
(335) . . . c = 0, 78 ± 0, 03. 0. * * . ! . hW. . . . k. *
(336) ( . . . . . . 1. •. . A. . . 1992<. •. . B. . . 1992 # * . . '') . .
(337) ,,. / > * . * * . . ;. *" . * -
(338) " ( Q . c<. . Q . I. . A * A 4 ? . B. ( * * * * . B". (.
(339)
(340) . ≤ 1992 15, 3 ± 0, 3 0, 54 ± 0, 02 0, 78 ± 0, 01. Q . # . a b c. . -
(341) . . . > 1992 11, 1 ± 0, 6 0, 11 ± 0, 06 0, 80 ± 0, 02. # . . " 8" "& "% " . A. B. hW. 0 & "% % " 8" . k a. "& . / > ( * * . . ( . . .
(342) " . . 5 ( . * . hW 1. . ( ( . w. A. h = 10 7 . ; P (h ) * .
(343) 8" ( * ;. . . A. . * . . (. k. 4 1. . . w. . . w". . k = 9hW ;
(344) 5 * (" . . w " W. . W. (. a1. ai. 7. 7 *. . k. . G *. ai 8 . a1. 4. . . w. 4 1. . . * * . + . " . ( ( . . w. . %. . hA a1 = 108". ∀hW .. k = 9, . ( . ai. k. . . hW. " . . . -. ;. " . .
(345)
(346) . . ! "" 44. hW. k. -
(347) . " . . . ( . 3"
(348) 9 & " - . ; "% < "& = "& " " .
(349)
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(352) ,,. - + P . *. W. . - " F. R .
(353) ,, %
(354) K&" . * * . H - . * 1. P . ( . - ( . . . ? .
(355) . Wt. . AB. * 1. . A - B. k < 500. 7 . * . . ;. . - . . . . . k > 500. ( . '' ( . 8. H * (
(356) ,, . 11.983.
(357) ,, 7 ( . - + 2. 1988. . 19898. 4 . 29.738. %. 3 . *" * ( - . = . < 2 =. * + . k". . - * . . . . . 7 . 3 * ( . hW 8. ? . . ( 7D" " " ( " 8" ; . 7. " . D". " " 8.
(358)
(359) .
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(362)
(363) . " / * . . " . ;. . . . . . . . . . " . . 1 -. . . . * . ;. *. . . . ( . . 1. . . . ( . J. - * . . . ". * (. 7 8 J. * . -. (" . ** * * . . . . ( .. . . . . . . . C . * ( . 1 + ( 2. ; = . 2 =.
(364) * . . *. * 1 ;. " " C . * ( < . . - ? . . .
(365)
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(367) &" 0 D %
(368)
(369) &" . . * . . . ( - . < - . . *. . * *. .
(370) ''& ( %&. -
(371)
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