Visualização e Análise de Redes Sociais

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    \f`jfmv lb Qjvrmij{mc b M`ijvb lb Tblbv Vcfjmjv

    Emtfcv Orjinbteb Fmvvcim|c lb Cijqbjtm

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    J`|tclrc

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    C xtbvb`|b mt|joc ljvfcttb vcdtb mioremv lbv|mv |f`jfmv bqjlb`fjm`lc xmt|jfrimtjlmlbv)xc`|cv act|bv b ijej|mbv }rb |e fc`|tjdrlc xmtm lb|btej`mt mv xtbabt`fjmv lbm`mijv|mv lc vb|ct C acfc `mv fmtmf|btv|jfmv lb fmlm eclbic lb tbxtbvb`|mc)mdv|b`lc%vb lm ljvfrvvc vcdtb m rvmdjijlmlb lcv vca|wmtbv }rb mv jexibeb`|me b

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    vrxct|me m m`ijvb lb tblbv vcfjmjv Bv|bv vca|wmtbv j`firbe eclbicv lb qjvrmij{mc bljqbtvmv abttmeb`|mv xmtm ftjmc) bljc b em`jxrimc lb otajfcv b vbrv fcexc`b`|bvfcec }rm`|c m vrm xcvjc `c xim`c) |mem`nc) {cce) actem|c) fct) cxmfjlmlb)

    bvxbvvrtm lb ij`nmv) motrxmeb`|cv) motbombv) b|f) mie lb e|clcv lb m`ijvbbv|m|v|jfm b cr|tmv ar`fjc`mijlmlbv |bjv C mt|joc ljvfr|b bv|tj|meb`|b mv |f`jfmv lbqjvrmij{mc .tbxtbvb`|mc otajfm*) obtmieb`|b) cdkb|cv fb`|tmjv .cr tbvri|mlcv* lbv|bvvca|wmtbv

    Mv |f`jfmv lb qjvrmij{mc lb tblbv vcfjmjv |e mxijfmdjijlmlb `m m`ijvb bfcer`jfmc lb bv|tr|rtmv vcfjmjv lb eclc obtmi7 c }rb jexijfm lj{bt be |bexcv m|rmjv}rb `c vbtqbe b~firvjqmeb`|b mc bv|rlc lcv |c be qcom vbtqjcv c`ij`b lbtbimfjc`meb`|c vcfjmi) ljvxc`qbjv xrdijfmeb`|b `m J`|bt`b| Cdqjmeb`|b }rb |mede mbv|bv) xcte) emjv lc }rb jvvc) vbtqbe mc bv|rlc obtmi lb m|ctbv b vrmv tbimbv `mvljqbtvmv bv|tr|rtmv vcfjmjv }rb `cv fcextbb`lbe) vbkme bv|mv tbimbv lb ebtfmlc) lb

    maj`jlmlb cr mej{mlb) lb lbxb`l`fjm cr j`air`fjm) lb fcimdctmc) b`|tb |m`|mv cr|tmvjemoj`qbjvc`ij`b cr caaij`b Bv|rlcv fb`|tmlcv be m|ctbv qjvme jlb`|jajfmt mvxbf|cvfcec fb`|tmijlmlb) xtbv|ojc b xmxjv lbvbexb`nmlcv vb bv|c emjv jvcimlcv cr vbjvcime vrdfc`kr`|cv lb m|ctbv) vb fccxbtme cr j`|botme7 cr mj`lm fmtmf|btv|jfmvxc`|rmjv lc tbimfjc`meb`|c b`|tb lcjv .lmlb* cr |tv .|tmlb* m|ctbv) cr ebvecvrdfc`kr`|cv emjctbv) cdvbtqm`lc mvxbf|cv bv|tr|rtmjv) otmr lb jormilmlb b`|tbxmt|jfjxm`|bv) tbfjxtcfjlmlb) |tm`vj|jqjlmlb) ljv|`fjm b mifm`fb b`|tb m|ctbv) cfctt`fjmlb fij}rbv) fcbvc) b|f @m cr|tm xc`|m b`fc`|tme%vb mv mxijfmbv fb`|tmlmv `mjlb`|jajfmc b tbfc`nbfjeb`|c lb otrxcv b ctom`j{mbv) c`lb bv|mv i|jemvfmtmf|btv|jfmv lb m`ijvb vc xtblcej`m`|bv `c bv|rlc lb fctxctmbv) fcer`jlmlbv)ocqbt`cv) j`v|j|rjbv blrfmfjc`mjv) lb vmlb) tbijojcvmv) amfbv ftjej`cvmv) b|f7

    friej`m`lc) `c ijej|b) m| `c bv|rlc lb bv|tr|rtmv mj`lm emjctbv) emjv lb`vmv bfcexib~mv fcec bfc`cejmv b vcfjblmlbv) c`lb |b`l`fjmv emjv emftc vc b`acfmlmv

    Dmvjfmeb`|b) cv eclbicv lb tbxtbvb`|mc lb tblbv vcfjmjv |e c xmxbi lb fcer`jfmtbv|tr|rtmv lbvvm `m|rtb{m b b~xict%imv) m aje lb b`|b`l%imv Xmtm |m`|c) b`qciqbe cvfc`fbj|cv bvvb`fjmjv lb m|ct) cr j`ljqlrc) xclb`lc mj`lm vbt rem ctom`j{mc crcdkb|c) b lb tbimc .cr ij`g) cr bic) cr mj`lm fc`b~c* b`|tb bv|bv m|ctbv7 jv|c )tbimfjc`meb`|c) j`|btmc Mxijfme |f`jfmv lb fc`v|trc b b~xictmc otajfmar`lmeb`|mlmv be |bctjmv b bv|rlcv lb rvmdjijlmlb) fco`jc) maactlm`fbv7 b bqcirbelbv|bv fc`fbj|cv xmtm cr|tcv) |mjv fcec c lb motrxmeb`|c cr fcer`jlmlb) lb`vjlmlb)xmxjv) fb`|tmijlmlb) fcbvc) b`|tb cr|tcv

    @bv|b bv|rlc) am{becv rem ft|jfm lmv lrmv xtj`fjxmjv |f`jfmv lb tbxtbvb`|mc lbtblbv vcfjmjv) cv eclbicv @clb%ij`g b eclbicv dmvbmlcv be em|tj{bv) vrdvjljmlcv xct|tmdmincv oictjcvcv lb Ij`|c` Atbbem`) }rb |mede `cv mr~jijcr `re tbvom|b njv|tjfcb b`|b`ljeb`|c lb cr|tcv e|clcv lb tbxtbvb`|mc) tbfb`|beb`|b fc`|tjdrj`lc mc imlclb Ritjg Dtm`lbv b cr|tcv) mie lb Ecnmeeml Onc`jbe b Kbm`%Lm`jbi Abgb|b @mvb}r`fjm) `bv|b ebvec bexb`nc lb ljvfrvvc b jlb`|jajfmc lb qm`|mob`v blbvqm`|mob`v) mdctlmecv |f`jfmv qmtjm`|bv cr ndtjlmv lbv|mv xtjebjtmv) |mjv fcecEm|Ij`g b @clb\tj~) xmtm mv }rmjv mv fc`|tjdrjbv tbfb`|bv lb @m|nmijb Nb`tz)`cqmeb`|b Kbm`%Lm`jbi Abgb|b) b cr|tcv actme jextbvfj`lqbjv C e|clc fc`vjv|b`|bbe tbqjvc djdijcotajfm b fc`atc`|mbv m`mi|jfmv tbvvmiqm c mvxbf|c ljmi|jfc xbic }rmimioremv |f`jfmv krv|jajfmtme cr|tmv b be }rb ebljlm b jexct|`fjm |f`jfmv xmtmibimv

    ecv|tmtme%vb fcexibeb`|mtbv cr fc`fcttb`|bv

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    Cv xtcdibemv emjv tbfcttb`|bv `cv }rmjv vb bexb`nme bv|mv |f`jfmv mdctlme }rbv|bvfcec m b~jv|`fjm lb tbimc cr `c b`|tb lcjv cr emjv m|ctbv jv|c ) c mifm`fb7 cfmej`nc cr ljv|`fjm }rb vb xtbfjvm xbtfcttbt b`|tb bibv7 m lb`vjlmlb lm bv|tr|rtm

    .}rm`|jlmlb eljm lb fc`b~bv xct m|ct*7 m cfctt`fjm lb motrxmeb`|cv .firv|btv)fcer`jlmlbv) xm`bij`nmv) j`|btbvvbv fcer`v* b xcvvjdjijlmlb cr `bfbvvjlmlb lbmotbombv .lb m|tjdr|cv j`ljqjlrmjv) tbxtbvb`|m`lc%cv r`jfmeb`|b*7 m fc`fb`|tmclbv|bv otrxcv .emjv icfmij{mlcv cr emjv bvxmtvcv*7 mie lb fb`|tmijlmlb) xtbv|ojc)xmxjv) v|m|rv lb m|ctbv `m tblb7 b) aj`mieb`|b) fcbvc) fc`kr`|c lb fmtmf|btv|jfmv lbimcv lb r`jc b`|tb m|ctbv }rb lb`c|me actm lb tbimfjc`meb`|c b ctlbe vcfjmi Mv}rbv|bv lm lb`vjlmlb) ljv|tjdrjc lb `v .}rb tbxtbvb`|me m|ctbv lm tblb* b fmej`ncvvc xmt|jfrimteb`|b jexct|m`|bv `m fc`v|trc lmv tbxtbvb`|mbv lb tblbv vcfjmjv xcv|c}rb |e vb ecv|tmlc lb|btej`m`|bv act|bv lb vrfbvvc lb rvmdjijlmlb) b xct}rb bedmvmem`ijvbv lc xmtmljoem fc`nbfjlc fcec Er`lc Xb}rb`c) frkmv bv|tr|rtmv vcfjmjv vbmxtbvb`|me oicdmieb`|b bvxmtvmv b icfmieb`|b lb`vmv) b }rb fmtmf|btj{me tblbv

    vbfrimtbv lb tbimfjc`meb`|c) |mjv fcec m}rbimv vbtqjlmv c`ij`b xct xtcqblctbv fcecAmfbdccg) \wj||bt) Ij`gblJ`) Occoib' b qtjcv cr|tcv

    Xtbfjvmeb`|b m b~xicvc lb tblbv lbv|b |jxc fce cv vbtqjcv c`ij`b lb tbimfjc`meb`|c)fmlm qb{ emjctbv) emjv ctom`j{mlcv b mdtm`ob`|bv) tbactm m cxct|r`jlmlb xmtmljvfrvvc lmv |f`jfmv lb tbxtbvb`|mc b m`ijvb lb tblbv vcfjmjv C Amfbdccg) xctb~bexic) bv|jemlc mifm`mt m emtfm lb re djinc lb rvrtjcv be mocv|c lb 48=4 W=U7mc \wj||bt) Ij`gblJ` b Occoib' k vc ftblj|mlmv emtfmv |mede vrdv|m`fjmjv tbvxbf|jqmeb`|b) 488 ejinbv .Mdt#48==* W4U) =88 ejinbv .Emt#48==* W6U b 1? ejinbv.@cq#48==* W

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    xmt|jfrimteb`|b) c xmxbi ar`lmeb`|mi lb mioctj|ecv lb c|jej{mc b#cr j`|btamfbvj`|btm|jqmv }rb vjexijaj}rbe |mtbamv ijomlmv m`ijvb) tbfc`nbfjeb`|c b tbxtbvb`|mclb vrdfc`kr`|cv emjv lb`vcv .fcer`jlmlbv b motrxmeb`|cv*) mie lm `bfbvvjlmlb lb

    `cqcv e|clcv lb tbxtbvb`|mc bv||jfm lb tbvri|mlcv }rb vrxbtbe mv ljajfrilmlbv lbqjvrmij{mc nckb |tm|mlmv mxb`mv lj`mejfmeb`|b

    Xtj`fjxmjv |f`jfmv lb tbxtbvb`|mc otajfm .@clb%ij`g b Em|tj~%dmvbl* btbxtbvb`|mbv qmtjm`|bv cr ndtjlmv

    Cv eclbicv @clb%ij`g) fmtmf|btj{mlcv ar`lmeb`|mieb`|b xct qt|jfbv .cr `v*ljvxcv|cv `re xim`c eri|jljeb`vjc`mi b j`|btijomlcv xct fc`b~bv .ij`gv* vjedcij{m`lctbimbv) |e vjlc j`ljvfr|jqbieb`|b mv emjv amejijmtbv b fc`v|m`|bv tbxtbvb`|mbv lbotmacv be obtmi) b xmt|jfrimteb`|b lmv tblbv vcfjmjv) fc`acteb lcfreb`|mlc xctAtbbem` W2U }rb vj`|b|j{cr bv|rlcv b b~bexicv lmv fj`fjmv vcfjmjv lm|mlcv lbvlb m

    lfmlm lb =:68 b }rb bextbomqme j`|b`vmeb`|b bv|m actem lb tbxtbvb`|mc Cvqt|jfbv vjedcij{me m|ctbv cr j`ljqlrcv lm bv|tr|rtm vcfjmi xtblcej`m`|beb`|b)xclb`lc vjedcij{mt |mede cdkb|cv) fmtmf|btv|jfmv) otrxcv) j`|btbvvbv cr }rmjv}rbtbibeb`|cv mvvcfjqbjv Fcereb`|b) vc tbxtbvb`|mlcv `re ebvec otajfc be actemv)fctbv) |mem`ncv) xcvjbv cr babj|cv ljv|j`|cv) fcec mt|jafjc xmtm lb`c|mt fimvvbv)vbebinm`mv) motrxmeb`|cv cr v|m|rv Mv fc`b~bv) xct vrm qb{) fcer`jfme mvxcvvqbjv tbimbv b~jv|b`|bv b`|tb cv m|ctbv) b) m`micomeb`|b) bextbome |medeqmtjmbv lb actem) fct cr bvxbvvrtm fmxm{bv lb ljv|j`orjt) `bvvb fmvc) |jxc cr otmr lbtbimfjc`meb`|c) cr cr|tmv fmtmf|btv|jfmv7 cr) mj`lm) xclbe |mede vbt tbxtbvb`|mlcvxct vb|mv .otmacv ctjb`|mlcv* be qb{ lb ijombv vjexibv) vjedcij{m`lc mvxbf|cvmljfjc`mjv jexifj|cv `m ljtbc lm fc`b~c b~jv|b`|b b`|tb lcjv m|ctbv) |mjv fcec) xct

    b~bexic) `rem tblb lb fc`nbfjeb`|cv) }rm`lc re m|ct M }rb fc`nbfb D) xcte D `cfc`nbfb M

    M Ajortm = jirv|tm rem tbxtbvb`|mc @clb%ij`g vjexibv dmvbmlm `rem tblb `cctjb`|mlm M|ctbv vc vjedcij{mlcv xct ftfricv m{rjv b mv tbimbv xct |tmcvfc`bf|m`lc%cv K mv Ajortmv 4 b 6 b~bexijajfme otajfcv @clb%ij`g `cv }rmjv)tbvxbf|jqmeb`|b) fctbv .4%m*) actemv .4%d* b |mem`ncv .4%f* lcv `v mkrlme qjvrmij{mtfimvvbv ljv|j`|mv lb m|ctbv b) `m vb}r`fjm) |jxcv ljv|j`|cv lb tbimbv b`|tb m|ctbv xctfctbv .6%m* b bvxbvvrtmv .6%d* ljv|j`|mv `mv fc`b~bv @m Ajortm 4%l b~bexijajfmecv mfcer`jfmc lb j`actembv mljfjc`mjv xbim tbxtbvb`|mc lcv `v `m actem lb otajfcvlb xj{{m7 fmlm re mtem{b`m`lc lmlcv bvxbfajfcv lc ` }rb tbxtbvb`|m

    Ajortm = Otmac `clb%ij`g .`c ctjb`|mlc*

    Mv ajortmv lb 4 m < actme mlmx|mlmv lb rem vtjb cabtbfjlm xct Im`b Nmttjvc` W1U

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    Ajortm 4 B~bexicv lb otmacv `clb%ij`g .`c ctjb`|mlcv* fce tbxtbvb`|mc lb`v be fctbv .m*) actemv .d* b |mem`ncv .f* ljabtb`|bv Be .l* j`actembvmljfjc`mjv vc fcer`jfmlmv `m tbxtbvb`|mc lcv `v be actem lb otajfcvlb xj{{m

    Ajortm 6 B~bexicv lb otmacv `clb%ij`g .`c ctjb`|mlcv* fce tbxtbvb`|mc lbtbimbv be fctbv .m* b bvxbvvrtmv .d* ljabtb`|bv

    Re b~bexic lb otmac ctjb`|mlc jirv|tmlc `m Ajortm

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    Ajortm 2 B~bexicv fc`ftb|cv lb tbxtbvb`|mc lb m|ctbv b tbimbv) dmvbmlmvbe |f`jfm @clb%ij`g

    Dtm`lbv b| mi W>U mlmx|mtme lb em`bjtm j`|btbvvm`|b re b~bexic lb Gtmfgnmtl| .=::1*vcdtb fcec xclbe vbt |bjv mv tbxtbvb`|mbv @clb%ij`g xmtm mxijfmbv xt|jfmv vbdbe ctjb`|mlmv `m m`ijvb lm bv|tr|rtm vcfjmi .tbxtclr{jlc `m Ajortm 1* Be 1%m rembv|tr|rtm ctom`j{mfjc`mi lb rem r`jlmlb lb mrlj|ctjm j`|bt`m lb rem otm`lb bextbvm tbxtbvb`|mlm `re @clb%ij`g njbtt}rjfc C obtb`|b lc lbxmt|meb`|c tbxtbvb`|mlc bem{ri) vrxbtqjvctbv be qbtebinc) mrlj|ctbv be qbtlb b vbftb|tjmv be memtbic Mxvj`lmomc lcv fcimdctmlctbv vcdtb m }rbe tbfcttjme ljm`|b lb }rbv|bv lb |tmdminc) re`cqc ljmotmem ctjb`|mlc acj obtmlc fce fc`b~bv moctm tbxtbvb`|mlmv xct vb|mvvjedcij{m`lc mv tbvxcv|mv mxtbvb`|mlmv xct fmlm ar`fjc`tjc .1%d* M jlb`|jajfmc lb

    }rb mioremv xbvvcmv) emjv tb}rjvj|mlmv lc }rb cr|tmv) |mi fcec m vbftb|tjm @m`fz)xcvvjdjij|cr m tbxtbvb`|mc lb rem `cqm bv|tr|rtm lb tbimbv b`|tb cv ar`fjc`tjcv)lb`c|m`lc rem bvxfjb lb njbtmt}rjm j`actemi `c lbxmt|meb`|c C tbvri|mlc tbxtclr{jlc be 1%f M|ctbv actme tbxcvjfjc`mlcv lb eclc m mxmtbfbtbe emjv bibqmlcv}rm`lc erj|c tb}rjvj|mlcv be }rbv|bv lb |tmdminc) b emjv dmj~c) fmvc fc`|ttjc

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    Ajortm 1 Tbxtbvb`|mbv @clb%ij`g lmv tbimbv njbt}rjfmv actemjv .m* bj`actemjv .d b f*

    Xmtm bv|tr|rtmv tbim|jqmeb`|b bvxmtvmv fcec mv jirv|tmlmv m| m}rj) tbxtbvb`|mbv lc|jxc @clb%ij`g |e vb ecv|tmlc dmv|m`|b mlb}rmlmv) ebljlm }rb vc b~|tbemeb`|bvjexibv) afbjv b j`|rj|jqmv) tb}rbtb`lc xcrfc cr `b`nre mxtb`lj{mlc xtqjc Ljm`|b lbbv|tr|rtmv emjv lb`vmv) `c b`|m`|c) fce erj|mv tbimbv b`|tb cv `v) m rvmdjijlmlb xtbkrljfmlm mc xmvvc be }rb cfcttbe erj|cv ftr{meb`|cv b`|tb ij`gv b cr|tmv actemv lbvcdtbxcvjc b`|tb bibeb`|cv Be vrm fcexmtmc lm ibojdjijlmlb lb otajfcv @clb%ij`g qbtvrv tbxtbvb`|mbv dmvbmlmv be em|tj{bv) Onc`jbe b| mi W:U ecv|tme fcec) ebljlm }rb c |mem`nc lc otajfc ftbvfb cr m lb`vjlmlb lmv fc`b~bv vb bibqm) rvrtjcv|e ljajfrilmlb lb b~xictmt qjvrmieb`|b c otajfc @clb%ij`g cr j`|btmojt fce vbrvbibeb`|cv) mj`lm }rb vrxct|mlcv xct tbfrtvcv fcexr|mfjc`mjv mqm`mlcv }rb beribe)xct b~bexic) ljv|tjdrjc b `mqbomc |tjljeb`vjc`mi Onc`jbe b| mi W:U |medefnmeme m m|b`c xmtm cv j`vrajfjb`|bv bvactcv lb cr|tcv mr|ctbv xmtm m|b`rmt |mjvljajfrilmlbv ijlm`lc fce |f`jfmv lb ibjmr|b dmvbmlmv be tbotmv bv||jfmv) |mjv fcecej`jej{mc lc `ebtc lb ftr{meb`|cv) ej`jej{mc lm tm{c b`|tb mv fc`b~bv emjvb~|b`vm b emjv frt|m lc otajfc) b tbqbimc lb vjeb|tjmv7 be }rmi}rbt lcv fmvcv)ebinctjmv tmtmeb`|b qmijlmlmv lb re xc`|c lb qjv|m fco`j|jqc

    M Ajortm ? b~bexijajfm c rvc lb tbxtbvb`|mbv @clb%ij`g xmtm fcer`jfmc lbbv|tr|rtmv lb`vmv) fce erj|mv fc`b~bv) c`lb) ebvec fce xcrfcv `v .`c emjv lc}rb 48 `mv lrmv jirv|tmbv*) m| |mtbamv tbim|jqmeb`|b vjexibv ajfme xtbkrljfmlmv

    lbqjlc v vcdtbxcvjbv lb cdkb|cv Be ?%m) re b~bexic vjexibv lb => erinbtbvtbimfjc`mlmv b`|tb vj) mlmx|mlc lb Atbbem` W=8U7 b) be ?%d) rem jirv|tmc lb Ej|fnbi

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    .=::) b~|tmlc lb Nbbt ! Dczl W==U @bvvb fmvc) c otajfc obtmlc xbicvca|wmtb lb m`ijvb lb tblbv vcfjmjv Qj{v|bt) dmvbmlc be eclbicv @clb%ij`g) xtcfrtmvjedcij{mt j`ljqlrcv `c xim`c fce ac|cv vrmv tbxtbvb`|m`lc%cv) `m j`|b`c lb m|b`rmtmv ljajfrilmlbv lb tbfc`nbfjeb`|c) bedctm vbe erj|c vrfbvvc ebljlm }rb erj|mvvcdtbxcvjbv xtbkrljfme m qjvrmij{mc

    Ajortm ? Tbxtbvb`|mbv `clb%ij`g lb bv|tr|rtmv emjv lb`vmv

    Ajortm > Otmac `clb%ij`g obtmlc xbic Qj{v|bt) vca|wmtb lb m`ijvb lb tblbvvcfjmjv % m|ctbv vc tbxtbvb`|mlcv xct ac|cv

    B~bexicv lb |b`|m|jqmv lb tbxtbvb`|mc |tjljeb`vjc`mi lb ljmotmemv @clb%ij`g fcecmt|jafjc lb m|b`rmc lc babj|c `bom|jqc lmv vcdtbxcvjbv vc jirv|tmlcv `mv Ajortmv :b =8 @m Ajortm :) tbxtclr{jlm lb Atbbem` W2U) mxb`mv re eclbic |tjljeb`vjc`mi

    vjexibv vrobtj`lc fcec m xbtvxbf|jqm xclb vbt bextbomlm K `m Ajortm =8 W?U)jirv|tmbv |tjljeb`vjc`mjv lb bv|tr|rtmv emjv vjexibv .=8%m* b emjv lb`vmv .=8%d*) c`lb

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    `cqmeb`|b xtcdibemv lb rvmdjijlmlb xclbe vbt cdvbtqmlcv lbqjlc vcdtbxcvjc lbbibeb`|cv ebvec ljvxcv|cv be xbtvxbf|jqm @m|rtmieb`|b }rb) be eclbicv 6L) bv|mvijej|mbv vc m|b`rmlmv xct j`|btamfbv j`|btm|jqmv }rb xbtej|me mkrv|bv lb xbtvxbf|jqm)

    xtcar`ljlmlb b {cce `mv jemob`v7 xcte) vbe otm`lbv qm`|mob`v xmtm tbxtbvb`|mbvbv||jfmv fcec be xmxbi

    Ajortm : Eclbic |tjljeb`vjc`mi vjexibv vrobtj`lc fcec m xbtvxbf|jqm xclbvbt bextbomlm `m tbxtbvb`|mc lb ljmotmemv @clb%ij`g

    Ajortm =8 B~bexicv lb tbxtbvb`|mbv @clb%ij`g |tjljeb`vjc`mjv emjv vjexibvbe .m* b emjv lb`vm be .d*

    Cr|tm ljajfrilmlb mvvcfjmlm mcv eclbicv @clb%ij`g tbvjlb `m aminm xbtfbxc lmv

    bqb`|rmjv xcvvjdjijlmlbv b~jv|b`|bv lb motrxmeb`|cv `m tblb vcfjmi m`mijvmlm)xc|b`fjmieb`|b lbxb`lb`|b lb erj|mv xbter|mbv `mv xcvjbv lcv `v Xtcdibemvtbim|jqcv ljv|tjdrjc lb `v `re xim`c fce dmvb be fmtmf|btv|jfmv j`|t`vbfmv |mjvfcec c tbfc`nbfjeb`|c lb fij}rbv b`qciqbe m`ijvb fcedj`m|tjm b vc vmdjlmeb`|b@X%Fcexib|cv) `c fmvc obtmi Lmlm) xct|m`|c) m j`amf|jdjijlmlb lcv erj|cv mioctj|ecvlb m`ijvb b fc`v|trc lb bv|tr|rtmv fcexib~mv lb otmacv be |btecv |jecv) v |f`jfmvlb tbxtbvb`|mc qjvrmi lb tblbv vcfjmjv vc tb}rbtjlmv }rb cabtbme ebinctbv tbvxcv|mvfco`j|jqmv vcd c eb`ct bvactc fcexr|mfjc`mi xcvvqbi7 |mtbamv bv|mv `mv }rmjv cveclbicv @clb%ij`g aminme fm|boctjfmeb`|b) vcdtb|rlc `m tbxtbvb`|mc lb tblbvotm`lbv b lb`vmv

    Be fc`|tmxcvjc) |f`jfmv dmvbmlmv be em|tj{bv .em|tj~%dmvbl* xmtm tbxtbvb`|mcotajfm lb tblbv vcfjmjv actme vrobtjlmv fcec mi|bt`m|jqmv mcv xtcdibemv lb cfirvcemtfm`|bv lcv ljmotmemv @clb%ij`g) ecv|tm`lc%vb emjv mlb}rmlmv xmtm otajfcv

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    otm`lbv b lb`vcv Cv qt|jfbv .cr m|ctbv lm tblb* vc tbxtbvb`|mlcv `cv bj~cv .nctj{c`|mib qbt|jfmi* lm em|tj{7 mv firimv tbabtb`fjmlmv xbimv fcctlb`mlmv .cr) j`|btvbbv lb fmlmfcir`m b ij`nm* mtem{b`me qmictbv dccibm`cv b~xtbvvm`lc m b~jv|`fjm cr `c lb

    tbimc b`|tb lcjv m|ctbv M xmt|jt lb }rmi}rbt xc`|c) vrfbvvjqmv xbter|mbv `mvfcctlb`mlmv .ij`nm) fcir`m* tbqbime mv tbimbv b bv|tr|rtmv vrdvb}rb`|bv lm tblb Xmtmebinct qjvrmij{mc) qmictbv vc `ctemieb`|b cej|jlcv }rm`lc amivcv xmtm m b~jv|`fjmlb fc`b~bv) b lbv|mfmlcv be fmvc fc`|ttjc M`micomeb`|b mcv eclbicv @clb%ij`g)fctbv) bv|jicv) vedcicv cr fc`bv vc mlej|jlcv xmtm fcer`jfmt j`actembv mljfjc`mjv)bedctm eb`cv fcer`v

    @mv tbxtbvb`|mbv Em|tj~%dmvbl emjv |tmljfjc`mjv) xmtm otmacv lb ijomc vjexibv .`cctjb`|mlcv*) qt|jfbv vc m`c|mlcv lrximeb`|b `mv ij`nmv b fcir`mv lb rem em|tj{}rmltmlm) tbvri|m`lc be j`actembv vje|tjfmv xmtm medmv mv tbojbv cxcv|mv lmljmoc`mi .lbij`bmlm xbic b`fc`|tc lb fmlm ` fce bib ebvec*7 jexijfm`lc) mvvje) }rb m

    em|tj{ }rb tbxtbvb`|m tbimbv vcfjmjv r`qcfmv fc`|b`lc m|ctbv tbxtbvb`|mlcvlrximeb`|b |m`|c `mv ij`nmv }rm`|c `mv fcir`mv b}rjqmib`|b vrm |tm`vxcv|m Bvvmactem lb tbxtbvb`|mc jirv|tmlm `m Ajortm ==

    Ajortm == Tbxtbvb`|mbv vjexibv @clb%ij`g .m* b Em|tj~%dmvbl .d* lb remebvem tblb vcfjmi

    Xmtm bv|tr|rtmv fc`|b`lc tbimbv ljtbfjc`mlmv .otmacv ctjb`|mlcv*) cv vb`|jlcv lbqjvrmij{mc lc otajfc .fcir`m xmtm ij`nm cr ij`nm xmtm fcir`m* fcer`jfmej`actembv) fc`acteb jirv|tmlc `m Ajortm =4) lb eclc }rb mv emtfmbv tbxtbvb`|mexmtbv ctlb`mlcv Cr|tmv qmtjmbv xclbe mj`lm vbt cd|jlmv xmtm vrxct|mt) xct b~bexic)tbxtbvb`|mc lb tbimfjc`meb`|cv b`|tb fimvvbv ljv|j`|mv .Ajortm =6*) |mjv fcec b`|tb|m`|mv cr|tmv jemoj`qbjv tblbv vcfjmjv lb ljabtb`|bv o`btcv .emvfrij`c b abej`j`c*

    cr lb mvvcfjmbv b`|tb mr|ctbv b xrdijfmbv) be }rb fmlm rem lbv|mv fimvvbv.emvfrij`c b abej`j`c cr mr|ct b xrdijfmc* m`c|mlm fcttbvxc`lb`|beb`|b `re lcvbj~cv .qbt|jfmi cr nctj{c`|mi* lm em|tj{) jexijfm`lc) `bvvb fmvc) em|tj{bv `c`bfbvvmtjmeb`|b }rmltmlmv) cdqjmeb`|b

    Bvvm jlbjm lb tbxtbvb`|mc em|tjfjmi lb fimvvbv ljv|j`|mv vrobtb |mede m xcvvjdjijlmlblb fc`v|trbv bextbom`lc%vb emjv ljeb`vbv `c bvxmc) fcec em|tj{bv fdjfmv)xmtmibicotejfmv cr vijlmv xcijljeb`vjc`mjv) erj|c bedctm tmtmeb`|b qjv|mv) xcv|c }rbvcatbtjme lmv ebvemv jexijfmbv lb vcdtbxcvjc cdvbtqmlmv `cv eclbicv @clb%ij`g

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    Ajortm =4 Tbxtbvb`|mbv vjexibv @clb%ij`g .m* b Em|tj~%dmvbl .d* lb remebvem tblb vcfjmi lb tbimbv ctjb`|mlmv

    Ajortm =6 Tbxtbvb`|mbv @clb%ij`g .m* b Em|tj~%dmvbl .d* lb tbimfjc`meb`|cvb`|tb m|ctbv lb lrmv fimvvbv ljv|j`|mv

    Mxbvmt lm ami|m lb amejijmtjlmlb lb erj|cv rvrtjcv fce cv eclbicv em|tjfjmjv xmtmtbxtbvb`|mc lb tblbv vcfjmjv) bv|rlcv |e lbec`v|tmlc vrm vrxbtjctjlmlb lbv|bv betbimc mcv eclbicv @clb%ij`g) xmt|jfrimteb`|b `m ebljlm be }rb vbr mvxbf|c ij`bmt bvje|tjfc `m ljv|tjdrjc lmv j`actembv amqctbfb) xmtm bv|tr|rtmv erj|c otm`lbv blb`vmv) m jlb`|jajfmc cr fc`|mobe lb `v b fc`b~bv) b cd|b`c lb j`actembvfcttbim|mv |mjv fcec tbfc`nbfjeb`|c lb fb`|tmijlmlb lb`|tb m|ctbv b jlb`|jajfmc lbqj{j`ncv fcer`v Onc`jbe b| mi W:U fj|me qtjcv |tmdmincv }rb bqjlb`fjme qm`|mob`vlmv tbxtbvb`|mbv otajfmv dmvbmlmv be em|tj{bv b cabtbfbe vrdvljcv bv|m|v|jfcvvrajfjb`|bv xmtm rem fc`firvc }rb vrobtb fcexibeb`|mtjlmlb b`|tb mv |f`jfmv lbtbxtbvb`|mc @clb%ij`g b em|tj~%dmvbl B`}rm`|c m xtjebjtm vb em`|be cxc emjvmlb}rmlm xmtm otajfcv eb`ctbv b emjv bvxmtvcv) m vbor`lm vrxct|m bv|tr|rtmv emjctbv b

    emjv lb`vmv lb em`bjtm emjv bab|jqm) fce tbvvmiqm tbmij{mc lb |mtbamv b`qciqb`lc|tjinmt fmej`ncv ljafbjv xmtm }rmi}rbt lmv |f`jfmv) bedctm ijobjtmeb`|b ebinctlbvbexb`nmlmv fce ljmotmemv @clb%ij`g

    Mv jirv|tmbv lm Ajortm =

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    Ajortm =

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    tbxtbvb`|mt xmtmibimeb`|b m tblb b c fc`kr`|c fcexibeb`|mt lmv fc`b~bv b`|tb qt|jfbvjv|c ) ij`gv b~jv|b`|b be re otajfc b ij`gv `c b~jv|b`|bv `c cr|tc M jlbjm lb |bt reljmotmem mr~jijmt }rb vb xtbv|b qbtjajfmc xmtm tblrc lb xtcdibemv lb rvmdjijlmlb

    be ebjc lb`vjlc lc otajfc xtj`fjxmi amfjieb`|b tbkbj|mlm ljm`|b lb fb`tjcv be}rb medcv cv ljmotmemv vb mxtbvb`|be ebljmeb`|b lb`vcv vj|rmc |tjqjmieb`|bb~bexijajfmlm `rem fcer`jlmlb frkc `ebtc lb ijombv ) vb`lc c`ebtc lb qt|jfbv medcv cv otajfcv .xtj`fjxmi b fcexibeb`|mt* vbtjme lb`vcv bcabtbfbtjme xtcdibemv lb rvmdjijlmlb

    Vnb` b| mi W=

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    Ajortm =2 \tv tbxtvb`|mbv lb rem ebvem tblb vcfjmi `c ctjb`|mlm blbv|m}rb lm tbxtbvb`|mc Em|Ij`g be .l*

    Ajortm =1 B~bexic lb tbxtbvb`|mc Em|Ij`g be em|tj{ vje|tjfm Fc`b~bv

    vc tbxtbvb`|mlmv `m j`|btvbc lb qt|jfbv lm em|tj{ b xct ij`nmv dtm`fmvijom`lc re qt|jfb m cr|tc Ijombv be qbtlb tbxtbvb`|me fmej`nc lb rem|ct m cr|tc

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    Rem `cqm |f`jfm lb tbxtbvb`|mc ndtjlm) fc`nbfjlm fcec @clb\tj~) acj b`|cj`|tclr{jlm xct Nb`tz b| mi W=6U) dmvbmlm bvvb`fjmieb`|b be @clb%ij`g fcefcer`jlmlbv) b`|tb|m`|c) tbxtbvb`|mlmv be em|tj{bv Mc fc`|ttjc lm Em|Ij`g) m

    fc`v|trc j`jfjm fce @clb%Ij`g .emjv vjexibv b j`|rj|jqm* b bqcirj xmtm em|tj{bv .emjvbajfm{bv `m tbxtbvb`|mc lb mi|mv lb`vjlmlbv* Mvvje) mv em|tj{bv fc`fb`|tme cvmotrxmeb`|cv cr fcer`jlmlbv .tbojbv emjv lb`vmv* b vbrv qt|jfbv vc fc`bf|mlcv.mvxbf|c bvxmtvc* mcv qt|jfbv lb cr|tmv em|tj{bv `m ebvem tbxtbvb`|mc) fc`actebjirv|tmlc `m Ajortm =? mc imlc lb rem tbxtbvb`|mc @clb%ij`g b}rjqmib`|b Mvjexijajfmc lb erj|mv fc`b~bv fcer`v b`|tb em|tj{bv be ij`nmv bvxbvvmv) mvvcfjmlmmc rvc lb fcictmc b mkrv|bv lb cxmfjlmlb) vrobtb vcirc xmtm c xtcdibem lbftr{meb`|c b`|tb ijombv b mj`lm mlej|b tbxtbvb`|mc lb m|tjdr|cv b j`actembvfcexibeb`|mtbv) fc`acteb jirv|tmlc `m Ajortm => M fmtom mvvcfjmlm jlb`|jajfmc bctom`j{mc em`rmi lcv otrxcv vbtjm ej`jej{mlm bedctm `c tbvciqjlm fcevca|wmtbv }rb xcvvjdjij|me xbter|mbv b`|tb m|ctbv b otrxcv) xct fijfm%icv b mttmv|m%icv

    lb rem xcvjc m cr|tm) lb eclc }rb mv fc`vb}rb`|bv tbfc`v|trbv qjvrmjv xmtbfbefc`|tjdrjt `m jlb`|jajfmc lb mvxbf|cv fcec fb`|tmijlmlb b fcbvc

    Ajortm =? Tbxtbvb`|mbv @clb%ij`g .m* b @c|b\tj~ .d* lb rem ebvem tblbvcfjmi `c ctjb`|mlm

    Ajortm => Ljmotmemv @clb\tj~ fce tbxtbvb`|mc lmv fc`b~bv .m*motbomlmv7 .d* vcdtbxcv|mv7 .f* vcdtbxcv|mv b xtbb`fnjlmv7 .l* vcdtbxcv|mv)xtbb`fnjlmv b fmttbom`lc m|tjdr|cv

    C bv|rlc mxtbvb`|mlc vrobtb tbvri|mlcv xtcejvvctbv m xmt|jt lcv b`vmjcv tbmij{mlcv beimdctm|tjc) xcte) fcec mlej|jlc xbicv xtxtjcv mr|ctbv) fmtbfjm mj`lm lbb~xbtjeb`|mc lb fmexc Fc`|rlc) m |f`jfm @clb\tj~ xmtbfb aminmt jebljm|meb`|bbe mc eb`cv lcjv xc`|cv; .m* ljafji lbfjvc lb motrxmeb`|c lb m|ctbv }rb xmt|jfjxmelb emjv lb rem fcer`jlmlb .medjorjlmlb lb motrxmeb`|c*7 b .d* tbv|tjc jextbvvc

    lb tbvri|mlcv vcd dmj~m tbvcircxclb`lc vjo`jajfmt re |tmlb%caa b`|tb cfri|mc lmvtbimbv ftr{mlmv qbtvrv ibojdjijlmlb lm jextbvvc Bv|m i|jem xcvvjqbieb`|b |tm|mlm

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    fcec lb eb`ct tbibq`fjm b`}rm`|c ebjcv eb`cv bv||jfcv xrlbtbe vbt fc`vjlbtmlcvrem cxc) b m xtjebjtm) mie lb `c b~firvjqmeb`|b |cfm`|b |f`jfm @clb\tj~) |bqbxtcxcv|m lb m|b`rmc mxtbvb`|mlm xbim xtxtjm Nb`tz b| mi be 488> W=?U) m|tmqv lm

    lrxijfmc lb `v lb mvvcfjmc medorm Ljtb|tj{bv fnbomtme m vbt cabtbfjlmv xmtm mlbfjvc lb }rm`lc lrxijfmt cr `c `v be tbxtbvb`|mbv @clb\tj~) xcv|c }rb) xmtmmior`v fmvcv xc`|rmjv) bv|m ebljlm xclb) be qb{ lb mkrlmt) xtbkrljfmt cr|tmv |mtbamv lbj`|btxtb|mc lcv otajfcv

    M lbvxbj|c lb e|clcv mi|bt`m|jqcv b vbrv |jecv tbvri|mlcv) ajfm bqjlb`|b m jexct|`fjmlcv eclbicv @clb%ij`g xmtm mv |f`jfmv lb tbxtbvb`|mc b m`ijvb lb tblbv vcfjmjvFce |clmv mv vrmv ijej|mbv b mv k mxc`|mlmv qm`|mob`v xmtm tbxtbvb`|mbv dmvbmlmvbe em|tj{bv `m tbmij{mc lm emjctjm lmv |mtbamv) cv eclbicv @clb%ij`g xmtbfbe mj`lmj`airb`fjmt act|beb`|b mv ljabtb`|bv |f`jfmv J`ebtmv lbimv xtcxrvbtme b fc`|j`rme mxtcxct qmtjmbv lbv|m) cr m |e xtbvb`|b lb miorem actem be ebjc mcv vbrv xmltbv

    otajfcv lb tbxtbvb`|mc M }rmijlmlb lc tbfc`nbfjeb`|c vbej|jfc lcv xc`|cvj`|btfc`bf|mlcv vrobtb maactlm`fb) b `c xct mfmvc mv |m`|mv |f`jfmv b~jv|b`|bv mfmdmexct tbfcttbt m jlbjm fb`|tmi lcv @clb%ij`gv lb rem cr cr|tm actem

    Cr|tmv |f`jfmv lb tbxtbvb`|mc b m`ijvb lb bv|tr|rtmv vcfjmjv

    Mie lb @clb%ij`g xrtmeb`|b) tbxtbvb`|mbv dmvbmlmv be em|tj{bv) qmtjm`|bv kfj|mlmv b |f`jfmv ndtjlmv |mjv fcec Em|Ij`g b @clb\tj~) qtjcv cr|tcv eclbicvotajfcv xclbe vbt bextbomlcv `m tbxtbvb`|mc b m`ijvb lb tblbv vcfjmjv Ljmotmemvlb ljvxbtvc) xct b~bexic) mvvbebinme%vb m @clb%ij`gv vb`lc fmtmf|btj{mlcv xbimljvxcvjc lb `v `re xim`c vbe fc`b~bv b~xtbvvmv) `c b`|m`|c M Ajortm =: jirv|tmlrmv tbxtbvb`|mbv) xim`m .=:%m* b |tjljeb`vjc`mi .=:%d*) lb tblbv vcfjmjv xbim |f`jfm

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