#For each case of size in 1000, 10000, and 1000000, we give the choose_vectors useful to draw networks. The order is as follows:

BINARY TREES
#ch_1_or_u
#ch_1_or_v
#ch_u_or_v
#ch_dxu_or_dxv
#choose_vector_dxu                dxu = D*(1+v)^2+x*D*dxv*(1+v)+x*D*(1+v)*dxv
#choose_vector_dxv                dxv = D*dxu*(1+u)+(1+u)*D*dxu
#ch_dyu_or_dyv
#choose_vector_dyv                dyv = (1+u)^2+D*dyu*(1+u)+D*(1+u)*dyu
#choose_vector_dyu                dyu = x*(1+v)^2+x*D*dyv*(1+v)+x*D*(1+v)*dyv

3-CONNECTED NETWORKS
#ch_K_in_dyK
#ch_dxK_in_dxyK
#ch_b_or_dxb
#ch_3b_or_dyb

NETWORKS
#choose_vector_non_trivial_D       nontrivialD  = S+P+H
#choose_vector_D                   D = y+S+P+H
#choose_vector_P                   P = y*(exp(S+H)-1)+(exp(S+H)-S-H-1)
#ch_y_or_P_or_H
#ch_S_or_H
#poisson_S_plus_H
#poisson_at_least1_S_plus_H
#poisson_at_least2_S_plus_H
#choose_vector_dD                  dD = dS+dP+dH
#choose_vector_dS                  dS = (dP+dH)*x*D+(y+P+H)*D+(y+P+H)*x*dD
#choose_vector_dP                  dP = y*(dS+dH)*exp(S+H)+(dS+dH)*(exp(S+H)-1)
#choose_vector_dH                  dH = dxK+dD*dyK
#ch_dP_or_dH
#ch_dS_or_dH
#choose_vector_ddD                 ddD = ddS+ddP+ddH
#choose_vector_ddS                 ddS =(ddP+ddH)*x*D+2*(dP+dH)*D+2*(dP+dH)*x*dD+2*(y+P+H)*dD+(y+P+H)*x*ddD
#choose_vector_ddP                 ddP=y*(ddS+ddH)*exp(S+H)+y*(dS+dH)^2*exp(S+H)+(ddS+ddH)*(exp(S+H)-1)+(dS+dH)^2*exp(S+H)
#choose_vector_ddH                 ddH=dxxK+2*dD*dxyK+ddD*dyK+dD^2*dyyK
#ch_ddP_or_ddH
#ch_ddS_or_ddH

case1000

0.6615414832803500035597979886227411601104 0.3384585167196499964402020113772588398896

0.2857117389214536767973417527718823881575 0.7142882610785463232026582472281176118425

0.1698805068332801282709774094231113691551 0.8301194931667198717290225905768886308449

0.2321398184753021101738000598195405010211 0.7678601815246978898261999401804594989787

0.03297221858038842987647190391784721465360 0.4835138907098057850617640480410763926730 0.4835138907098057850617640480410763926730

0.5 0.5

0.2286189060348950150332900248835184266217 0.7713810939651049849667099751164815733783

0.01966240304254261597679847666256329613845 0.4901687984787286920116007616687183519306 0.4901687984787286920116007616687183519306

0.01357676741068965153830850140283451797440 0.4932116162946551742308457492985827410129 0.4932116162946551742308457492985827410129

0.1023148450168439782698851645651737890839 0.8976851549831560217301148354348262109160

0.01056720808167383324019751492093784146016 0.9894327919183261667598024850790621585398

0.04311363388351982963897237807044101069163 0.9568863661164801703610276219295589893083

0.05196496216386519137788597254497784663637 0.9480350378361348086221140274550221533636

0.4660957179218444279557575080519119651348 0.5114068601310629668563001347837065047126 0.02249742194709260518794235716438153014876

0.9139878157865566664292213348398398820981 0.04008991075099080435300915856459467461758 0.04398722106161163705816901021027502516956 0.001935052400840892159600496385290418114481

0.9776951366508074895780032884764823019703 0.02230486334919251042199671152351769802201

0.9521598179071332961526783226032395304727 0.04582431370840708140589528364952032058903 0.002015868384459622441426393747240148938516

0.9539546913140707625282368689673626501555 0.04604530868592923747176313103263734984445

0.955061268674745207369030282137721749565 0.043913511679865593954736620352980661375 0.001009566910159365331537118597062809981 0.000015473223116672224086898482698644421 0.000000177863867572080425842240166461865 0.000000001635628473739856169023394177031 0.000000000012534307560736010128493170663 0.000000000000082332109321289267459850060 0.000000000000000473201584402709122385254 0.000000000000000002417523006134090139172 0.000000000000000000011115718776191682978 0.000000000000000000000046463487100364519 0.000000000000000000000000178031761799986 0.000000000000000000000000000629681700706 0.000000000000000000000000000002068044939 0.000000000000000000000000000000006339217 0.000000000000000000000000000000000018217

0.977186279737874066287399730432586990578 0.022465407464496135534004928612959310516 0.000344318200811702472925183527778544658 0.000003957919200805831320292647038449868 0.000000036396854684250090334729127932701 0.000000000278919924775267192904667620653 0.000000000001832096877087850514132097442 0.000000000000010529927535733034502715892 0.000000000000000053795978098195305925824 0.000000000000000000247352750030681007881 0.000000000000000000001033929657783926800 0.000000000000000000000003961655270404479 0.000000000000000000000000014012004392130 0.000000000000000000000000000046019210548 0.000000000000000000000000000000141063560 0.000000000000000000000000000000000405380 0.000000000000000000000000000000000001096

0.984732310485631417892066712490818569144 0.015092593266487989280245206578743308962 0.000173488547914587524951573077059062559 0.000001595393222414238110691408955889198 0.000000012225972860652389932954790563410 0.000000000080306800295495671166472254486 0.000000000000461561175237790262965662961 0.000000000000002358053727322342472292018 0.000000000000000010842280311524738519123 0.000000000000000000045320519665545262524 0.000000000000000000000173652312068601886 0.000000000000000000000000614191996357204 0.000000000000000000000000002017172561919 0.000000000000000000000000000006183277364 0.000000000000000000000000000000017769110 0.000000000000000000000000000000000048060 0.000000000000000000000000000000000000123

0.3890237728269593678814398154419828898371 0.5224693656626273963154848589311391252173 0.08850686151041323580307532562687798494541

0.06559227647181332533012995905935130885116 0.8313551248150918552029286005169347323890 0.1030525987130948194669414404237139587600

0.9569939078932783332146106674199199410492 0.04300609210672166678538933258008005895054

0.7662041853012229678832785377155320832899 0.2337958146987770321167214622844679167097

0.8551386165711708936181217118224947362810 0.1448613834288291063818782881775052637192

0.8146572070015435802281410071569352458382 0.1853427929984564197718589928430647541619

0.08861357849075398400821966071265393354459 0.5248214384927513459979176506026979858613 0.3865649830164946699938626886846480805948

0.4295431639979207567175927561672647080475 0.04380007889359697698740838905423973264620 0.005429342791178045721135191338052590178828 0.06881468667676750906233697202569426144446 0.4524127276405367115115266914147487076826

0.9480124438913205036436956522607205794070 0.004692539799824630079412761853232248335722 0.04260247650903023619747882403281492392081 0.004692539799824630079412761853232248335722

0.5526733385906650026654778640143494960751 0.3424656176505172821628029503703286590996 0.05352925045561084002241885159027808433276 0.05133179330320687514930033402504376049241

0.5758495256311288285690935226182953220606 0.4241504743688711714309064773817046779392

0.1864847989136442137746712115068253003222 0.8135152010863557862253287884931746996778





case10000

0.6554828694400191053580522747732445925295 0.3445171305599808946419477252267554074703

0.2819599570144786861812161244742556502535 0.7180400429855213138187838755257443497465

0.1710805300771953607079513563155294593528 0.8289194699228046392920486436844705406471

0.2304939245683050361465251644551291253195 0.7695060754316949638534748355448708746805

0.01049161905385143899819365011607635612020 0.4947541904730742805009031749419618219402 0.4947541904730742805009031749419618219402

0.5 0.5

0.2293906138654120815232837852494691211930 0.7706093861345879184767162147505308788070

0.006211608192538779629341215804977867173054 0.4968941959037306101853293920975110664143 0.4968941959037306101853293920975110664143

0.004306762784306981741738802945977214580052 0.4978466186078465091291305985270113927098 0.4978466186078465091291305985270113927098

0.09883853176333715697807141072472118277958 0.9011614682366628430219285892752788172202

0.003397034693621610456156423239028744632851 0.9966029653063783895438435767609712553671

0.01393816364406663508364967218297299948272 0.9860618363559333649163503278170270005176

0.01702895461509294433999731957283858317466 0.9829710453849070556600026804271614168254

0.4660448236292321853614485334179461733415 0.5114140646637983264311148619749228459781 0.02254111170696948820743660460713098068369

0.9139366196864386281104912070364764757454 0.04010939289916924293617899073458986103253 0.04401402314486474333057564685670586595701 0.001939964269527385622754155372227797265320

0.9776813633952326097847671846753714434841 0.02231863660476739021523281532462855651010

0.9521258078009664929348742134536965641811 0.04585316578708987607635843706755243285302 0.002021026411943630988767349478751002965920

0.9538645915145742239513048725846731731260 0.04613540848542577604869512741532682687414

0.955033317494253709119515893483749064533 0.043940177262072136631791825852513513128 0.001010822943270739962818857166081760308 0.000015502335012569877931879985043362988 0.000000178311933194007718391353571328455 0.000000001640792589947440480172161653088 0.000000000012581885178230753233245318564 0.000000000000082697229344989211671547318 0.000000000000000475602637355492472215642 0.000000000000000002431336257989890726636 0.000000000000000000011186347554876979547 0.000000000000000000000046788476616243016 0.000000000000000000000000179391119894307 0.000000000000000000000000000634893485108 0.000000000000000000000000000002086489083 0.000000000000000000000000000000006399826 0.000000000000000000000000000000000018403

0.977171870672403347137770276050154308050 0.022479375549698756008932742714462508266 0.000344751583810721083321990372490465894 0.000003965423359199808487208836463147532 0.000000036489073654427667618006088768199 0.000000000279804612595623760760418502814 0.000000000001839077840230293516755023592 0.000000000000010576778424663977085903430 0.000000000000000054069727240367139516776 0.000000000000000000248769687500239239580 0.000000000000000000001040514309906316040 0.000000000000000000000003989423054978156 0.000000000000000000000000014119197808888 0.000000000000000000000000000046400778692 0.000000000000000000000000000000142323722 0.000000000000000000000000000000000409261 0.000000000000000000000000000000000001108

0.984722630010848388831470393927543242766 0.015102051458678000904319546726326667639 0.000173707766514449151785570562714844134 0.000001598425921405503093019046815083726 0.000000012257010137811480980984480099343 0.000000000080561916127181489351259701623 0.000000000000463322170331225344334182157 0.000000000000002368557075546391447789137 0.000000000000000010897506489920947482710 0.000000000000000000045580358117581308754 0.000000000000000000000174759087690789904 0.000000000000000000000000618499992104888 0.000000000000000000000000002032614150122 0.000000000000000000000000000006234576632 0.000000000000000000000000000000017927935 0.000000000000000000000000000000000048520 0.000000000000000000000000000000000000124

0.3862963395495335154733611776464861931944 0.5224833412528731454402420532581254677337 0.09122031919759333908639676909538833907221

0.06638385475909259006305056762499804994057 0.8297855136953394076237726209123564068939 0.1038306315455680023131768114626455431658

0.9569683098432193140552456035182382378718 0.04303169015678068594475439648176176212726

0.7645710969244040241448556090942396682131 0.2354289030755959758551443909057603317866

0.8513609660880359813779854493338720087720 0.1486390339119640186220145506661279912281

0.8089693468769644302249933179035181290115 0.1910306531230355697750066820964818709886

0.08177687778782818023981013554890401765966 0.5232301115884210882174669271186293802501 0.3949930106237507315427229373324666020907

0.4691827602793510481103598755584386924187 0.01500199327176226582677229305103306407413 0.001877191647890522661286897042954924297164 0.02346453729603710040840218473407910458196 0.4904735175049590629931787496134942146281

0.9541080640361096369426195239803822024563 0.001494430786103185005212195219019941838093 0.04290307439168399304695608558157791386738 0.001494430786103185005212195219019941838093

0.5533555720999897237012340568654619137196 0.3404552770598381731840867021260544566476 0.05437032835842233517244585697887300062096 0.05181882248174976794223338402961062901201

0.5698289434575134172367965799050243636928 0.4301710565424865827632034200949756363072

0.1715227403733036038782044215405283005017 0.8284772596266963961217955784594716994983






case1000000

0.6529525103368191672650236505630386828934 0.3470474896631808327349763494369613171062

0.2803952249948665955847559187922054010592 0.7196047750051334044152440812077945989408

0.1715694615774611865476075467034987317219 0.8284305384225388134523924532965012682783

0.2298075295337431288271806705333212443183 0.7701924704662568711728193294666787556817

0.001051877139321583838793449251799591336900 0.4994740614303392080806032753741002043316 0.4994740614303392080806032753741002043316

0.5 0.5

0.2296976155984303891395260683966794360221 0.7703023844015696108604739316033205639779

0.0006209080082037969768000988903948216032355 0.4996895459958981015115999505548025891982 0.4996895459958981015115999505548025891982

0.0004312368895559450446099327656350388317413 0.4997843815552220274776950336171824805844 0.4997843815552220274776950336171824805844

0.09736382064286582607785119655750788825036 0.9026361793571341739221488034424921117496

0.0003420521338795178506359014551700761604649 0.9996579478661204821493640985448299238395

0.001406947274764814487953331488540655493322 0.9985930527252351855120466685114593445068

0.001729028296706593719284713911907770385886 0.9982709717032934062807152860880922296141

0.4660390463483958900966054586358933251695 0.5114148624402886335251618783591683374389 0.02254609121131547637823266300493833739631

0.9139309508396226896537707868453767905353 0.04011153759081544570580073793828548527298 0.04401699093672080208228049252804957907682 0.001940520632841062558147982688288145115344

0.9776798382709861098689898101231084030950 0.02232016172901389013101018987689159688628

0.9521220294134851903392556553145171273771 0.04585636004650411959540501051019333820209 0.002021610540010690065339334175289534420293

0.9538543245013054556181599882016395160176 0.04614567549869454438184001179836048398237

0.955030222421232247306303084518528824090 0.043943129928703732799427325320078724226 0.001010962073553750886689312725981037251 0.000015505560874131823483943041702353137 0.000000178361600531860737809817469983631 0.000000001641365226451677546742197212499 0.000000000012587162813124319138361616688 0.000000000000082737745278375867261630401 0.000000000000000475869166940883078683120 0.000000000000000002432870143910482673189 0.000000000000000000011194193264636701389 0.000000000000000000000046824590423369534 0.000000000000000000000000179542229181668 0.000000000000000000000000000635473043309 0.000000000000000000000000000002088540824 0.000000000000000000000000000000006406570 0.000000000000000000000000000000000018424 

0.977170275119422732949676243281663325132 0.022480922254573733708485028157866435309 0.000344799590057405435137259741654525375 0.000003966254896845948436700435828518574 0.000000036499296078943464189965291599558 0.000000000279902714463664209750498577516 0.000000000001839852223717469856525405426 0.000000000000010581977331494791256764207 0.000000000000000054100115119518618582322 0.000000000000000000248927032050120294453 0.000000000000000000001041245764254736299 0.000000000000000000000003992508721378192 0.000000000000000000000000014131113772924 0.000000000000000000000000000046443210007 0.000000000000000000000000000000142463904 0.000000000000000000000000000000000409693 0.000000000000000000000000000000000001109

0.984721558063965876371578449131034052852 0.015103098782883226486438342979609150092 0.000173732049667418447175007077095010947 0.000001598761976759334104576018539827795 0.000000012260450615495400380315553771721 0.000000000080590205678858263411897324975 0.000000000000463517514418124598461768974 0.000000000000002369722605178878345026515 0.000000000000000010903636962436578609616 0.000000000000000000045609212099642595608 0.000000000000000000000174882033938782998 0.000000000000000000000000618978715111310 0.000000000000000000000000002034330691672 0.000000000000000000000000000006240281253 0.000000000000000000000000000000017945603 0.000000000000000000000000000000000048572 0.000000000000000000000000000000000000124

0.3851460674398186034107226801507805019557 0.5224848887893838763468484577407355879553 0.09236904377079752024242886210848391008964

0.06671062749183899407897306600073569715327 0.8291430732678523522601991383863219464922 0.1041462992403086536608277956129423563552

0.9569654754198113448268853934226883952671 0.04303452458018865517311460657731160473234

0.7639082430114071319914736581843454218557 0.2360917569885928680085263418156545781441

0.8497707522399939853947748171909685824302 0.1502292477600060146052251828090314175700

0.8065630979999361951674428436866237835953 0.1934369020000638048325571563133762164049

0.07893042852785247889547584165404340078866 0.5225596810947290620566820713039135721855 0.3985098903774184590478420870420430270256

0.4876368452244434788667479715333324885184 0.001553773567657203488065862832599243424488 0.0001951650711995198140063498462056378695450 0.002425696969327791219453529695394379504738 0.5081885191673720066117262860924682506837

0.9566786417217719785348590760704876251646 0.0001498662728211460131055621047935842581067 0.04302162573258572943892979971992520631960 0.0001498662728211460131055621047935842581067

0.5536776484642325448672617015856960799926 0.3395853231910679259825006998372911937956 0.05472278194789704700546334525302004450125 0.05201424639680248214477425332399268171102

0.5673400764499480477762823368536737948122 0.4326599235500519522237176631463262051878

0.1653199895409610063617429172344163454896 0.8346800104590389936382570827655836545104



  



