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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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(223)     4     (         ". # . 81.669. 4      .   #  - .  .       . . .  . .   .    .   ** * .    ;.    . (    * 4 (.     (  *      2* = 7 4  ;.           "    *    ** *      * .   8< ( 6        . 2  =    2  = (    .  .   .   #  -      .     .   .  . -   4       '',  .  .   *.        .            -.  .   w  '()    t0   

(224)  &   w tf    μw 

(225) .      *   . .  ''1            .   *.  .         ** * (.   ** * . *  .  μw =. tf i=to +1. i hW w. tf − t0. ..  w  .   %   t

(226)  t0  tf      %

(227)

(228)  hWw   $

(229)   %   

(230)       

(231)    

(232)   * 

(233)   !!  

(234)  tf = t0 +5  %  

(235)   tf −t0 = 5 t.     *  .  .    .   ** *" .       .   G  1.    -.   .   .   ** *. μ.  (. 0 ≤ μ < 1. H.     *       ** *     *.  - .      . . . hW w.     .  .

(236) .   .   .   ** *. μ.  (. 1 ≤ μ < 2. C.        ** *      .

(237)

(238)  .   *. 

(239)     ' ()  !

(240)  .  - .       . . .   .  . .         ** *. μ.  (. μ ≥ 2. H -.  %.    *    ** *   (M      ;  *.  - .  . . / I  .  < -   4.      . .     . 2.2.       .     *  .  .  . 1993. 1994.    . . .     ''.   *   . 1995. 1996. . . 1997.   ** *. 1998. μ ,". 

(241) 

(242)  

(243)  

(244) . .    .  . . . t hW w. .

(245). . . .

(246). ,. . .

(247)

(248).  &        . " 

(249). . ",).   . / 0  "" "%    & "  &&& .

(250) 

(251)   . " .     . Gt.     .  . . . .    * . B  *  (.     *    .    .         "  .    .     .   * .    .  

(252)        . (     . -  *  . .   +

(253)  

(254)  , . 4     .      *     - 2  ** =.   * . / >      I .  . .      . 3.1.    . .  *  1.  /  * ( *  ''K 

(255) ,,  - +  4    *. 5 . 1995.   . 7309".    *. 

(256) ,, . *  . 11983.  .

(257)   ''K.  .      .      .   '' 

(258) ,,  .   .     4   . *  *   - +  .     ** .   .     **  . 5.     * . .   I. 3.1. *. C . .  . . .   .

(259)

(260)  .  . 1  . . - 

(261) . ""   . . 2  "& "   . &      ". . . . . . . . . . . . . .  . . . . . .  . . . . . . .  . . . . . . . . . . . .  . . . . .  .  . . .  .  . .  . . . . . .  . .  . . . . .  . . .  . . . . . . . .  . . .  . . . . . .  . .  .  .  . .  . . . . . . .  .   . .   "  " &      "   -,  (   ". .        .  ""     " 3" "    "        .     1      & "  -,  .  &     .

(262)

(263)  . - 

(264) .          +     . .    *.  .   (   +   + .         -;. -   **  .     (M "   .   (     - +" (   (  "  2.  = (    . K H          7. 1990 ≤ t ≤ 19928.     *.    .  . . !      . !      7t.  .         - +     ** *     . .  .   . > 199281.   (.

(265)

(266)   . - 

(267) . .   +

(268)  

(269)  ,.         .   ** *.  * ?      ."   . μ.      .

(270) ".    . &   ** * .     (    ** * #   -   .  . P (μ).    .

(271) 

(272) "              +. ("    . w. .     " . / >   

(273)     *       . .    .  .     * .        - .     . .  * .  ''.  <. '',  ''      *  . . .   *. /   (  . ''     + ( .  * . P (μ).   (1. . .  '', . μw = μ. μ>2.  4. * .     '',  . 4    ?    -.        *  C  G  .   .         .  *    .  .   

(274) . P (μ).  ("  &&& .  " "    4  *. μ.  &    .

(275)

(276)  . - 

(277) . .

(278)       .    .

(279)  (  (      1 .     .  * . ''"   (     *    . . . 2 = .    .  .  ''

(280) . .   ** * .    (.       . P (μ).

(281)

(282)  . - 

(283) . .    .          .  .  .    .

(284) 

(285) .            .         +  .  .  .  '' .     . .     . 

(286) ,, #  *   -.  .    . . ;. W   Gt  Gt      "    .  * .      . / >       -     . P (hA )" P (hW )  P (k).  *   ''" '') 

(287) ,,    . (  *     4   (            *     H ;   -    .          . P (hA ).     . 4 . .     ?  .    *   .  .  .  >    ;.  *  1. P (hA ) (       ( (    ".  *"    5;7"  10   15<    *   .      . hA = 10 . 4    .     .   H .   . 10.  " . . 20%.   < - .. 9    *          * . P (hW )            ; P (hW ) = α(hW )−γ  α = 0, 68 ± 0, 01  γ = 2, 33 ± 0, 03 /.

(288)       . I 

(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)

(350)  . - 

(351) . .     .     / >   )     *   2.   =     (  ;  .  . Gt. GW t. . . t = 2001.   <       . 3 .  .    .  . k".    .    .           .     ( . h. . .  .  <.   .        5   .   "      " 

(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)  .  

(360) . - 

(361) . '" "  "%   3. Gt. . GW t.  . t = 2001.

(362) 

(363)   . " /   *   .         .                   "  . ;.       . .   . .  . . .  .   . "    .     .      1 -.   . . . *     .     ;.  *.    . . . (     . . 1.            .      .    .  (   .  J.   -   *        .  .   .  ". *        (.      7   8      J. * .  -.       ("    .   ** *   *   .  .    .  .    (   .. .   .         . .   .     .   . C      .         *          ( .  1    +         (  2. ;  =  . 2  =.

(364)    *          .        .    *.   *     1        ;.   "   "    C .     *         (       <    .  .   -         ?   .  .  .

(365)

(366)  *.  . .   *  B "  **  H ;5.  %

(367) &"   0   D %

(368)

(369) &" .    . *      .   .     . (      -      . < -   .    .      *.        . * *.     .

(370) ''& ( %&. -  

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(379) 

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