jaale vidnyan

jaale vidnyan heey eka shaikshanik kshetra aahe jeey dursanchar jaale, sanganak jaale, jaivik jaale, sandnyanatmak aanee shabdarth jaale aanee samajik jaale yasarkhya jatil jaalecha abhyas karate, jyamadhye 'nodes' (kinwa 'shirobindu') dware darshavilele vegale ghatak kinwa ghatak aanee ghatak kinwa abhinetyanmadhil sambandhancha 'duve' (kinwa 'kadaa') mhanoon vichar keela jaato. ganitatil aalekh siddhant, bhautikshastratil sankhyikeey yantriki, sanganak vidnyanatil mahitee utkhanan aanee mahitee drushyikaran, sankhyikitil anumanatmak pratirupan aanee samajshastratil samajik sanrachanesah siddhant aanee paddhatinvar heey kshetra aadharit aahe. united states national research kaunsilane network sciencechi vyakhya ashee kelee aahe qee "yaa ghatananchya purvanumey namunyankade namunyankade bhautik, jaivik aanee samajik ghatananchya network pratinidhitvancha abhyas."
parshvabhoomi aanee itihas.
jatil sambandhatmak mahitiche vishleshan karnyache sadhan mhanoon vividh shakhanmadhye jaalyancha abhyas udayas aala aahe. yaa kshetratil sarvat juna dnyat pepper mhanje 1736 madhye leonhard ulerne lihilele konigsbergche prasiddha saat pool. yoolarche shirobindu aanee kathanche ganiteey varnan haah aalekh siddhantacha paya hota, joou ganitachi eka shakha aahe jee jaale sanrachanet jodiwar sambandhanchya gunadharmancha abhyas karate. aalekh siddhantachya kshetracha vikas suruch rahila aanee rasayanshastrat tyache upayog aadhalale (sylvester, 1878).
hungarian ganitshastradnya aanee pradhyapak danes kanig yanni 1936 madhye 'theary auph finite andd infinite graphs' yaa shirshakakhali aalekh siddhantatil pahile pustak lihile.
1930 chya dashakat, gestalt paramparetil manasshastradnya jacob moreno americet aale. tyanni samajshastra vikasit kele aanee april 1933 madhye vaidyakeey vidvananchya parishadet teey lokansamor sadar kele. morenone assa dawa keela qee "samajshastrachya aagmanapurvi konalahi 'tantotant' gatachi aantarvaiyaktik rachana kashee disate heey mahit navhate" (moreno, 1953). samajshastra heey prathamik shaletil vidyarthyanchya gatachya samajik sanrachaneche pratinidhitva hote. eka mulga vagalata, jyaa eka muleela eka mulgi aavadate asey mhanat hota, tyaa mulanchi mule mitra hotee aanee mulee mulinchi mitra hotee. bhavna paraspar purak navhati. samajik sanrachaneche heey jaale pratinidhitva itake rochak aadhalale qee teey newyork timesmadhye (3 april 1933, prushth 17) chhapale gele. samajshastrala anek upayog sapadale aahet aanee teey samajik jaalyanchya vishleshanachya kshetrat vikasit jhaale aahe.
network vidnyanatil sambhavyata siddhant haah aalekh siddhantacha eka bhag mhanoon paul erdos aanee alfried renee yanchya yadruchchik aalekhavaril aath prasiddha shodhanibandhansah vikasit jhaala. samajik networksathi ghatankiy yadruchchik aalekh model kinwa pii * hii eka sanketik chaukat aahe jee samajik networkmadhye jaalemadhye taychya sambhavyatechya jaageche pratinidhitva karnyasathi vaparali jaate. jaale sambhavyata sanrachanancha paryayi drushtikon mhanje jaale sambhavyata matricks, joou jaalechya namunyatil kathachya aitihasik upasthitivar kinwa anupasthitivar aadharit jaalemadhye jaalemadhye kadaa sambhavyateche model banavato.
1998 madhye, david crackhardt aanee cathleen carley yanni pii. see. aii. aine. models meta-networkchi kalpana mandali. teey suchavatat qee "serve sanstha yaa teen kshetranmadhye, vyakti, karye aanee sansadhananmadhye sanrachit aahet". tyanchya peparne hii sankalpana sadar kelee qee network anek kshetranmadhye aadhaltat aanee teey ekmekanshi sambandhit aahet. heey kshetra gatishil jaale vishleshan navachya jaale vidnyanachya aanakhi eka upashakhet vikasit jhaale aahe.
agadi alikadech itar jaale vidnyan prayatnanmadhye vividh jaale topologyche ganiteey varnan karnyavar laksh kendrit kele aahe. dunken wats aanee steven strogatz yanni lahan-jaagtik jaalyache varnan karat, ganitachya pratinidhitvasaha jaalyanvaril anubhavjanya mahitiche samanvay kele. albert-lezlo barabasi aanee reka albert yanni scale-free networkcha shodh lavala, eka assa gunadharm joou vastavik network habmadhye anek lahan degree shirobindusaha sahastitva aahe heey satya tipato aanee yaa scale-free sthitiche mool spasht karnyasathi eka gatishil model sadar karato.
sanrakshn upkram vibhag.
yuu.ess. 1996 madhye jaalyanchya vidnyanavar aadharit eka parichalan sankalpana mhanoon jaalyanchya kendrasthani asalelya yuddhat lashkarala pratham rus nirman jhaala. johnn aii. parmentola, yuu.ess. sanshodhan aanee prayogshala vyavasthapanasathichya lashkari sanchalakanni 1 december 2003 roji lashkarachya vidnyan aanee tantradnyan mandalala (bast) network vidnyan heey lashkarache naveen sanshodhan kshetra bananyacha prastav mandala. rashtriy akadamichya rashtriy sanshodhan parishadesathi (aine. aar. see.) abhiyantriki aanee bhautik vidnyan vibhag, haah lashkarasathi mahattvachya vidnyan aanee tantradnyanachya muddyanvar charcha karnyasathi eka sanyojak pradhikaran mhanoon kaam karato aanee rashtriy akadmindware aayojit swatantra lashkari-sambandhit abhyasanvar dekhrekh thevato. moolbhut sanshodhan, jaale vidnyanatil tapasache naveen kshetra olakhane aanee tyasathi nidhi puravine, jaale-kendrit karye aanee jaalechya moolbhut dnyanachi sadhyachi adim sthitee sakaranyasathi aavashyak asaleli daree door karnyat madat karoo shakate qaa heey shodhanyasathi yaa sansthene eka abhyas keela.
parinami, yaa bastney 2005 madhye network science (varr sandarbhit) yaa shirshakacha aine. aar. see. abhyas jaaree keela, jyane lashkarasathi network vidnyanatil moolbhut sanshodhanache naveen kshetra paribhashit kele. tyaa abhyasache nishkarsh aanee shifarshinchya aadhare aanee tyanantarchya 2007 chya aine. aar. see. chya ahavalavar aadharit, network vidnyan, tantradnyan aanee prayogansathichya lashkari kendrasathi dhoran, lashkarachya moolbhut sanshodhan sansadhananna network vidnyanat eka naveen moolbhut sanshodhan karyakram suru karnyasathi punarnirdeshit karnyat aale. jatil jaalyansathi eka naveen saiddhantik paya tayar karnyasathi, lashkarachya prayogshalanmadhye sadhya suru asalelya kahee pramukh jaale vidnyan sanshodhan prayatnanche uddishtah
2004 madhye fredrick aay. yanni suruvat kelee. moxleyne david ess. kadey pathimbyachi vinanti kelee. alberts, sanrakshn vibhagane yuu. ess. chya sanyogane pahile jaale vidnyan kendra sthapan karnyas madat kelee.ess. united states miiliitary akadami (yu. ess. emm. aii.) yethe sainya. tyanchya margdarshanakhali dow. moxley aanee yuu. ess. emm. aii. chey pradhyapak, network vidnyanatil pahile aantarshakhiy padvi abhyaskram west pointvar cadetsna shikavale gele. bhavishyatil netyanchya tyanchya cadermadhye network vidnyanache siddhant adhik changlya prakare rujavanyasathi, yu. ess. emm. aii. neey network vidnyanat paach-abhyaskram padvipurv alpasankhyak dekhil sthapan kele aahe. 
2006 madhye, yuu.ess. lashkar aanee united kingdamne (yuu. keey.) sainya sanshodhan prayogshala, brittonche sanrakshn mantralay aanee yuu. keey. madheel udyog aanee vidyapithancha samooh yanchyatil eka sahyogi bhagidari, jaale aanee mahitee vidnyan aantarrashtriy tantradnyan yutee sthapan kelee.ess. aanee britton. donhi deshanchya garjanmadhye jaale-kendrit kamkajachya samarthanarth moolbhut sanshodhan karane heey yaa yutiche uddisht aahe.
2009 madhye, yuu.ess. lashkarane network science cta, lashkar sanshodhan prayogshala, serdec aanee yuu. ess. madheel sumare 30 audhyogik sanshodhan aanee vikas prayogshala aanee vidyapithancha eka sangh yanchyatil eka sahyogi sanshodhan yutee sthapan kelee.ess. paraspar jodalelya samajik/sandnyanatmak, mahitee aanee dalanvalan jaalyanmadhye antarbhut samanatanchi sakhol samaj vikasit karane aanee parinami anek prakarchya jaalyanche vishleshan, andaj, rachana aanee guntaguntichya pranalinvar prabhav takanyachi aapali kshamata sudharane heey yaa yutiche uddisht aahe.
tyanantar, yaa prayatnancha parinam mhanoon, yuu.ess. sanrakshn vibhagane network vidnyanala aadhar denare asankhya sanshodhan prakalp prayojit kele aahet.
jaale gunadharm.
anekada, jaalyanmadhye kahee vishisht vaishishtye asatat jee jaalyache gunadharm aanee vaishishtyanche vishleshan karnyasathi mojali jaau shakatat. yaa jaale gunadharmanche vartan anekada jaale pratikruti paribhashit karate aanee vishisht pratikruti ekmekanshi kashee viruddha aahet yache vishleshan karnyasathi vaparali jaau shakate. jaale vidnyanat vaparlya jaanarya itar sandnyanchya anek vyakhya aalekh siddhantachya shabdakoshat aadhalu shakatat.
aakar.
jaalyacha aakar haah nodeschya sankhyecha sandarbh gheu shakato, sootra 1 kinwa, qamee samanyatah, kadanchya sootra 2 chee sankhya, jee (bahu-kadaa nasalelya jodalelya aalekhasathi) sootra 3 (eka vruksh) teey sootra 4 (eka sampoorn aalekh) paryant asoo shakate. eka sadhya aalekhamadhye (eka jaale jyamadhye shirobindunchya pratyek jodimadhye jastit jaast eka (dishaheen) dhaar astitvat asate aanee jyamadhye shirobindu swatashi jodale jaat naheet), aaplyakade sootra 5 aahe; nirdeshit aalekhasathi (swa-jodalelya nodeshivay), sootra 6; swa-jodanyanna parvanagi asalelya nirdeshit aalekhasathi, sootra 7. aalekhchya paristhitit jyamadhye shirobindunchya jodimadhye anek kadaa asoo shakatat, sootra 8.
ghanata.
jaaleche ghanata sootra _ 9 heey sootra _ 2 chya kadanchya sankhyechya 0 aanee 1 darmyanche samanyikrut gunottar aanee sootra _ 1 nodes asalelya jaalemadhil sambhavya kadanchya sankhyeshi paribhashit kele jaate. jaalyachi ghanata heey jaalyamadhye astitvat asalelya aanee asha prakare mojalya jaau jaau 'paryayi' kadachya takkevariche mojmap aahe.
sootra _ 12
jethe sootra _ 13 aanee sootra _ 14 heey sootra _ 1 nodes jodalelya jaalyatil anukrame kiman aanee kamal kadaa aahet. sadhya aalekhanchya babatit, sootra _ 14 heey dwaimasik gunank sootra _ 17 aanee sootra _ 18 dware dile jaate, jeey ghanata dete.
sootra _ 19.
aanakhi eka sambhavya samikaran mhanje sootra 20 tarr sambandhanche sootra 21 ekdishatmak aahe (vassaraman aanee fost 1994). heey jaalyachya ghanatevar adhik changle vihangavalokan dete, kaaran ektarfi sambandh mojale jaau shakatat.
samtol jaalichi ghanata.
jaaleche ghanata sootra _ 9, jethe kadaa darmyan chhed nasato, teey sootra _ 1 nodes asalelya jaalemadhil sambhavya kadaa sankhyechya kathanchya sankhyechya sootra _ 2 chey gunottar mhanoon paribhashit kele jaate, jeey chhed naan tayar kadaa sootra _ 25 asalelya aalekhadvare dile jaate, sootra _ 26 dete.
sarasari padvi.
nodache degree sootra _ 27 heey tyachyashi jodalelya kadaa sankhya aahe. jaalyachya ghanateshi jawalun sambandhit sarasari degree, sootra _ 28 (kinwa, nirdeshit aalekhanchya babatit, sootra _ 29, done bhinn shirobindunchya degreemadhye yogdan yogdan dishaheen aalekhatil pratyek kathavarun udbhavnara 2 chaa purvicha ghatak). air yadruchchik aalekh modelmadhye (sootra _ 30) aapan sootra _ 31 chey apekshit moolya moju shakato (aniyantrit shirobinduchya sootra _ 27 chya apekshit mulyachya barobariche): yadruchchik shirobinduche sootra _ 3 networkmadhye itar shirobindu upalabdh asatat aanee sambhavyata sootra _ 34 saha, pratyekas jodale jaate. tyamule sootra _ 35.
sarasari sarvat lahan marg lambi (kinwa vaishishtyapurn marg lambi).
serve jodyanchya nodesmadhil sarvat lahan marg shodhun aanee tyachya lambichya serve marganvar sarasari gheuun (lambi hii margavar asalelya madhyavarti kadaa sankhya aahe, i.eae., aalekhatil done shirobindu sutranmadhil antar sootra _ 36 sootra _ 37). heey aaplyala, sarasari, jaalyachya eka sadasyakadun karya sadasyakade jaanyasathi kitee pavale lagatat heey darshavate. yadruchchik jaale pratikrutichya shirshanchya sankhyeche karya mhanoon apekshit sarasari sarvat lahan margachya lambiche (mhanje, sarasari sarvat lahan margachya lambichi ektrit sarasari) vartan, sootra _ 1 heey tyaa pratikruticha lahan-jaagtik prabhav darshavite qee nahee heey paribhashit karate; jarr tee sootra _ 39 mhanoon mojmap karat asel tarr pratikruti lahan-jaagtik jaali tayar karate. laghuganakapeksha jalad vadhisathi, heey model lahan vishva nirman karat nahee. sootra _ 40 chya vishesh prakaranala ultra-small world effect mhanoon olakhale jaate.
jaalyacha vyas.
jaale aalekh mojanyache aanakhi eka sadhan mhanoon, jaalecha vyas haah jaalemadhil mojalelya serve sarvat lahan marganpaiki sarvat lamb marg mhanoon aapan paribhashit karoo shakato. jaalyatil done sarvat durchya nodesmadhil heey sarvat qamee antar aahe. karya shabdant, pratyek nodapasoon itar serve nodesparyantchya sarvat lahan margachi lambi ekada mojali gelee qee, ganana kelelya serve margachya lambipaiki vyas sarvat lamb asato. vyas haah jaalyachya resheey aakarache pratinidhitva karato. jarr node a-b-c-d jodalela asel, tarr a-> d pasoon jaatana haah vyas 3 (3-hops, 3-links) asel.
samooh gunank.
samooh gunank heey 'serve-majhe-mitra-pratyek-mahit-itar' malmatteche mojmap aahe. majhe mitra majhe mitra asatat asey kadhikadhi yache varnan kele jaate. adhik tantotant, nodacha samooh gunank mhanje nodchya shejari ekmekanna aanee vidyaman duvyanche praman aanee asha duvyanchya jastit jaast shakya sankhyeche gunottar. sampoorn jaalyasathi samooh gunank haah serve nodeschya samooh gunankanchi sarasari aahe. jaalyasathi uchch samooh gunank haah eka chhotya jagacha aanakhi eka sanket aahe.
sootra _ 41 vya nodacha samooh gunank aahe
jethe sootra _ 43 heey sootra _ 41 vya nodchya shejarinchi sankhya aahe aanee sootra _ 45 heey yaa shejarimadhil jodanyanchi sankhya aahe. tevha, tevha sambandhanchi jastit jaast sambhavya sankhya ashee aahe,
jarr sootra _ 47 asel tarr aine. ell. pii. aii. heey baa modelmadhye qamee hote aanee tyala "resheey" mhanoon sambodhale jaate. jarr sootra _ 48 asel tarr aine. ell. pii. aii. laa "up-rekheey" mhanoon sambodhale jaate aanee jaalyache ansh vitaran vistarit ghatankiy vitaranakade jaate. jarr sootra _ 49 asel tarr aine. ell. pii. aii. laa 'atee-rekheey' asey sambodhale jaate aanee networkmadhil jawaljawal itar serve nodeshey thodya sankhyene nodes jodale jaatat. sootra _ 50 aanee sootra _ 49 yaa donhisathi, jaalyacha praman-mukt gunadharm anant pranali aakarachya maryadet modala jaato. tathapi, jarr sootra _ 52 heey sootra _ 53 peksha kinchit mothe asel, tarr aine. ell. pii. aii. mule padvi vitaran houu shakate jeey kshanik pramanat mukt asalyache disate.
madhyasthi-chalit sanlagnata (emm. dii. aii.) model.
madhyasthi-chalit sanlagnata (emm. dii. aii.) modelmadhye jyamadhye sootra _ 54 kadaa asalela naveen node yadruchchikpane vidyaman jodalela node nivadato aanee nantar swatah laa tyashi navhe tarr yadruchchikpane nivadalelya tyachya shejari sootra _ 54 saha jodato. sambhavyateche sootra _ 56 jeey nivadalele vidyaman nodache node sootra _ 41 aahe
ghatak sootra _ 59 heey harmonic madhya chey ulat aahe.
(ihm) sootrachya anshanche _ 43 node sootrachya shejari _ 41. vyapak sankhyatmak tapasani asey suchavate qee andaje sootra _ 62 sathee mothya sootra _ 1 maryadetil sarasari ihm moolya sthir hote jyacha arth sootra _ 64 assa hoto. yacha arth assa qee jitke jaast asel titke uchch
nodmadhye duve (degree) asatat, tyamule adhik duve milanyachi shakyata titakich jaast asate kaaran teey asoo shakatat
madhyasthandvare mothya sankhyene pohochane jeey moolatah antardnyani swaroop dharan karate
shrimantanchi kalpana adhik samruddha hote yantrana (kinwa barabasi-albert modelcha pradhanyacha sanlagnata niyam). tyamule emm. dii. aii. jaale anusaran kartana pahile jaau shakate
paa niyam parantu bhesat.
tathapi, sootra _ 65 sathee heey varnan karate qee vijeta serve yantrana gheto kaaran aaplyala aadhalate qee ekoon nodespacky jawaljawal sootra _ 66 madhye eka padvi asate aanee eka padvimadhye atee-samruddha aahe. sootra 54 chey moolya vadhalyane atee shrimant aanee garib yanchyatil vishamata qamee hote aanee sootra 68 mhanoon aaplyala shrimant teey atee shrimant aanee samruddha yanmadhye sankraman hote.
fitness model.
aanakhi eka model jethe mukhya ghatak mhanje shirobinduche swaroop aahe, teey caldarelli aanee itaranni sadar kele aahe. yethe done shirobindu sootra 69 darmyan eka duva tayar keela jaato, jyamadhye samavisht shirobinduchya tandurustichya _ 70 yaa jodani karya sutradvare sambhavyata dilee jaate.
shirobindu i chee degree dilee jaate 
jarr sootra _ 72 heey sootra _ 73 chey ulat aanee vadhanare karya asel, tarr
sambhavyata vitaran sootra _ 74 dware dile jaate
parinami, jarr tandurusti sootra _ 76 heey shakti niyam mhanoon vitarit kele gele, tarr nodchi padvi dekhil karate.
qamee antardnyanane jalad kshay hott asalelya sambhavyatechya vitaranasah
sootra _ 77 heey yaa prakarchya jodani karyasah ekatra
sootra 79 eka sthirank aanee sootra 80 heey havicide functions, aaplyala dekhil milate
praman-mukt jaale.
vividh nodes sootra _ 69 aanee tyaa prakarchya jodani karyasathi jee. dii. pii. chaa yogya vapar karoon rashtranmadhil vyaparache varnan karnyasathi asey model yashasviritya lagoo kele gele aahe.
network vishleshan.
samajik network vishleshan.
samajik jaalyanche vishleshan samajik sansthanmadhil sambandhanchya sanrachaneche parikshan karate. yaa sanstha sanstha vyakti asatat, parantu tyaa gut, sanstha, rashtra rajye, sanketsthale, vidvattapoorn prakashne dekhil asoo shakatat.
1970 chya dashakapasun, jaalyanchya anubhavjanya abhyasane samajik vidnyanat madhyavarti bhoomika bajavali aahe aanee jaalyanchya abhyasasathi vaparali jaanari anek ganiteey aanee sankhyikeey sadhane samajshastrat pratham vikasit kelee gelee aahet. itar anek anuprayoganmadhye, navkalpana, batamya aanee afavancha prasar samajoon ghenyasathi samajik network vishleshanacha vapar keela gela aahe. tyachpramane, rog aanee aarogyashi sambandhit vartane yaa donhincha prasar tapasanyasathi yacha vapar keela gela aahe. heey bajarachya abhyasasathi dekhil lagoo kele gele aahe, jithe vinimay sambandhanmadhil vishvasachi bhoomika aanee kimmati nishchit karnyat samajik yantraneche parikshan karnyasathi yacha vapar keela gela aahe. tyachpramane, rajkiy chalvali aanee samajik sanghatananmadhye bharaticha abhyas karnyasathi yacha vapar keela gela aahe. yacha vapar vaidnyanik matbhed tasech shaikshanik pratishthechi sankalpana tayar karnyasathi dekhil keela gela aahe. karya bhashechya sampadan sahityat, paradeshat abhyas tayar sanshodhanacha eka prasthapit itihas aahe, joou samvayask vidyarthyanchya parasparsanvadache jaale tyanchya bhashechya pragativar kassa prabhav takte heey ughad karato. agadi alikade, jaalyanchya vishleshanane (aanee tyachya jawalche natevaik rahdari vishleshanane) lashkari guptaheranmadhye, shrenibaddha aanee netrutvahin asha donhi prakarchya bandkhor jaalyancha pardafash karnyasathi lakshaniy vapar keela aahe. gunheshastrat, gunhegari tolhya, gunhegar chalval, saha-ullanghan, gunhegari karvayancha andaj lavane aanee dhorane tayar karane yanmadhil prabhavshali kalakaranna olakhanyasathi yacha vapar keela jaat aahe.
gatishil jaale vishleshan.
gatishil jaale vishleshan heey guntaguntichya samajik-tantrik pranalinchya prabhavanmadhil ghatakanchya vividh varganmadhil sambandhanchya badalatya sanrachaneche parikshan karate aanee samajik sthirata aanee naveen gut, vishay aanee netyanchya udayasarkhya badalanna pratibimbit karate. gatishil jaale vishleshan heey anek prakarchya nodes (ghatak) aanee anek prakarchya duvyanni banalelya meta-networkwar kendrit aahe. yaa sanstha atyant vaividhyapurn asoo shakatat. udaharananmadhye lock, sanstha, vishay, sansadhane, karye, karyakram, thikane aanee shraddha yancha samavesh hoto.
gatishil jaale tantre visheshtah cull aanee kalantarane jaalemadhil badalanche moolyankan karnyasathi, udayonmukh netyanchi olakh patvinyasathi aanee lock aanee kalpananchya saha-utkrantiche parikshan karnyasathi upayukt aahet.
jaivik jaale vishleshan.
sarvajanikaritya upalabdh asalelya uchch thruput jaivik mahitichya alikadil sphotamule, aanvik jaalyanchya vishleshanat lakshaniy swarasya vadhale aahe. yaa majkuratil vishleshanacha prakar samajik jaalyanchya vishleshanashi jawalun sambandhit aahe, parantu anekada jaalyatil sthanik namunyanvar laksh kendrit karato. udaharanarth, jaale rachana heey lahan uplekh asatat jeey jaalemadhye jaast pratinidhitva karatat. kriyakalap rachana yaa jaalyatil nodes aanee kadaa yanchya gunadharmanmadhye samaan atee-pratinidhitva namune aahet jeey jaalyachya sanrachanenusar jaast pratinidhitva karatat. jaivik jaalyanchya vishleshanamule jaalyachya aushadhacha vikas jhaala aahe, joou parasparsanvadatil rogancha parinam pahato.
link vishleshan.
jodani vishleshan haah jaale vishleshanacha eka upasanch aahe, joou vastunmadhil sambandhancha shodh gheto. yache udaharan asoo shakate, sanshayit aanee piditanche patte, tyanni dial kelele durdhvani kramank aanee dilelya kalmaryadet tyanni kelele aarthik vyavhar aanee police tapasacha eka bhag mhanoon yaa vishayanmadhil kautumbik sambandh tapasane. yethe duva vishleshan heey vegvegalya prakarchya anek vastunmadhil mahattvapoorn sambandh aanee sambandh pradan karate jeey mahitichya vegalya tukadyanvarun spasht hott naheet. fasavanuk shodhanyasathi banka aanee vima sansthandvare, dursanchar network vishleshanat dursanchar operatordware, mahamarishastra aanee aushadhashastratil vaidyakeey kshetradvare, kayadyachi amalbajavani tapasanit, prasangikta mulyankanasathi shodh injindware (aanee yaulat spamdexsathi spammersdware aanee shodh engine optimizationsathi vyavasay malkadware) aanee itar sarvatra jithe anek vastunmadhil sambandhanche vishleshan karave lagate, asha thikani sanganak-sahayyit kinwa purnapane svayanchalit sanganak-aadharit duva vishleshan adhikadhik vaparale jaate.
mahamariche vishleshan.
surr model heey sansargjanya loksankhyemadhye jaagtik mahamarichya prasaracha andaj lavnyasathi sarvat prasiddha algoridampaiki eka aahe.
sansarg honyachi shakyata.
vareel sootra sansargjanya loksankhyetil pratyek sanvedanshil ghatkasathi sansargachya "shakti" chey varnan karate, jithe teey rogachya sankraman darachya samatulya aahe.
sansargjanya loksankhyemadhye sanvedanshil lokanmadhil badalacha magova ghenyasathih
barey honyasathi sankramit.
kalantarane, sankramitanchi sankhya khalilpramane chadh-utaar karateh barey honyacha nirdisht darr, sootra 86 dware darshavila jaato parantu sarasari sansargjanya kalavadhichya sootra 87 peksha ekavar vaja keela jaato, sansargjanya vyaktinchi sankhya, sootra 88 aanee veleteel badal, sootra 89.
sansargjanya kalavadhi.
surr modelchya sandarbhat, mahamarimule loksankhyevar maat hoil qee nahee heey sootra _ 90 chya mulyavar avalambun asate kinwa sankramit vyaktine sankramit kelelya sarasari lokanvar avalambun asate."
web link vishleshan.
anek web shodh kramvariche kramvarit link-aadharit kendriyata metriksacha vapar keela jaato, jyat (disanyachya kramane) marchioricha hyper search, googalcha pagerank, clenbergcha hiit algoridam, cherank aanee trustrank algoridam yancha samavesh aahe. web prushthanchya sankalanachya sanrachanetun mahitee samajoon ghenyasathi aanee kadhanyasathi mahitee vidnyan aanee sampreshan vidnyanat dekhil duva vishleshan kele jaate. udaharanarth, heey vishleshan rajkarnyanchya sanketsthale kinwa blogg yanchyatil parasparsanvadache asoo shakate.
pagerank.
pagerank yadruchchikpane "nodes" kinwa websites nivadoon aanee nantar vishisht sambhavyatesah, itar nodeswar "yadruchchikpane udee maroon" karya karate. yaa itar nodesmadhye yadruchchikpane udee maroon, heey pagerankla network purnapane paar karnyas madat karate kaaran kahee vebprushthe parighavar astitvat aahet aanee tyanche moolyankan sahajpane kele jaanar nahee.
sootra _ 92 yaa pratyek nodmadhye prushthanchya sootra _ 93 chya berijdware paribhashit kelyapramane eka pagerank asato joou sootra _ 93 chya "mahatva" kinwa pagerankchya "out-degree" chya 93 putt kinwa sootrachya outlinkschya 41 putt ekashi jodato.
yadruchchik udee.
varr spasht kelyapramane, pagerank internetvaril pratyek sanketsthalavar pagerank niyukt karnyachya prayatnanmadhye yadruchchik udee soochibaddha karate. yaa yadruchchik udimule asha sanketsthale sapadatat jee samanya shodh paddhatinmadhye kadachit sapadanar naheet, jase qee rundi-pratham shodh aanee kholee-pratham shodh.
pagerank nishchit karnyasathi vareel sutrapeksha sudharananmadhye yaa yadruchchik udee ghatakanchi bharr ghalane samavisht aahe. yadruchchik udishivay, kahee prushthanna 0 chee pagerank milel jee changli nasel.
pahile mhanje sootra _ 52, kinwa yadruchchik udee lagnyachi sambhavyata. viruddha mhanje 'damping factor' kinwa sootra _ 99.
tyakade pahanyacha aanakhi eka margah
kendrikaranache upay.
aalekhatil nodes aanee kadaa yanchya sapeksh mahattvavishayichi mahitee samajik shastrasarkhya shakhanmadhye mothya pramanat vaparlya manalya kendriyatechya upayayojanandvare midavata yete. jevha jaale vishleshanala asha prashnanchi uttare dyavi lagatat tevha kendriyata upay aavashyak asatatah "jaalemadhil serve kinwa bahutek nodesmadhye sandesh kinwa mahitee pasarate yachee khatri karnyasathi jaalemadhil konatya nodesla lakshya kele pahije?"kinwa yaulat", rogacha prasar rokhanyasathi konatya nodesla lakshya kele pahije?". degree kendriyata, nikatata kendriyata, darmyanchi kendriyata, eigenwector kendriyata aanee katz kendriyata heey kendriyateche aupcharikpane sthapit upay aahet. jaalyachya vishleshanacha uddesh samanyatah konatya prakarchya kendriyatechya mojamapancha vapar karayacha heey tharvato.
jaalyanmadhye samagricha prasar.
jatil jaalyatil samagri done pramukh paddhatindware pasaru shakateh sanrakshit prasar aanee sanrakshit nasalela prasar. sanrakshit prasaramadhye, guntaguntichya jaalyamadhye pravesh karnari samagri jasjashi jaate tastashi tichi ekoon matra sthir rahate. sanrakshit prasarache model nalikanni jodalelya funnelchya maliket nishchit pramanat paanee paanee pichardware sarvottam prakare darshavile jaau shakate. yethe, ghagra mool strotache pratinidhitva karato aanee paanee mhanje pasaravale jaat asalele praman. funnell aanee aanee nalya anukrame nodes aanee nodesmadhil jodani darshavtat. jevha paanee eka nalitoon karya nalat jaate, tevha purvi panyachya samparkat asalelya nalitoon paanee lagech nahise hote. sanrakshit nasalelya prasaramadhye, samagriche praman badalate kaaran tee eka jatil jaalyatun pravesh karate aanee jaate. nalikanni jodalelya funnelchya maliketoon satat satat naladvare sanrakshit nasalelya prasarache model sarvottampane darshavile jaau shakate. yethe, mool strotatoon yenare paanee anant aahe. tasech, panyachya samparkat aalelya konatyahi fanelmadhye paanee satat fanelmadhye jaat asatanahi tyacha anubhav yet rahato. bahutek sansargjanya roganchya sankramanache spashtikaran denyasathi sanrakshit nasalele model sarvat yogya aahe.
surr model.
1927 madhye, doubleu. oo. carmack aanee aaa. jee. mcendrickne eka model tayar kele jyamadhye tyanni keval teen vibhag asaleli, sanvedanshil, eka nishchit loksankhya manalih formula _ 102, sankramit, formula _ 103 aanee punarprapt, formula _ 104. yaa modelsathi vaparlya jaanarya vibhaganmadhye teen varg asatatah
yaa pratikruticha pravah khalilpramane vicharat ghetala jaau shakatoh
nishchit loksankhyecha vapar karoon, formula _ 109, carmack aanee mcendrickne khaleel samikarane kadhalih
yaa samikarananchya nirmitimadhye anek gruhitke kelee geleeh pratham, loksankhyetil ekhadya vyaktila rogacha sansarg honyachi itar pratyek vyaktisarkhich shakyata, rogacha sampark kinwa sansarg darr manalya manalya 111 yaa sutrasah, manali gelee pahije. mhanoon, sankramit vyakti sampark sadhate aanee prati ekak vel sootra 112 itaransah rog prasarit karnyas saksham asate aanee sansargjanya asalelya sansarg jhalelya vyaktichya samparkancha ansh sootra 113 asato. nantar prati sansargjanya ekak velet naveen sansargachi sankhya sootra 114 asate, jeey sootra 115 mhanoon naveen sansargacha (kinwa atisanvedanshil shreni sodanare) darr dete (braur aanee castillo-shavez, 2001). karya aanee aanee samikaranansathi, sanvedanshil varg sodanari loksankhya hii sankramit vargat pravesh tayar sankhyechya barobarichi aahe asey samaja. tathapi, sansargjanya heey varg prati ekak vel sodat barey jhalelya/kadhoon takalelya vargat prati ekak vel 116 yaa darr sutrane pravesh karat aahet (jethe sootra 116 heey sarasari barey honyacha darr darshavate kinwa sootra 118 haah sarasari sansargjanya kalavadhi darshavate). ekach velee velee yaa prakriyanna samoohik kruticha niyam asey sambodhale jaate, hii eka vyapakpane sweekarli jaanari kalpana aahe qee loksankhyetil done gatanmadhil samparkacha darr sambandhit pratyek gatachya aakarachya pramanat asato (delly aanee gunny, 2005). shevati, asey manale jaate qee sansarg aanee barey honyacha darr janm aanee mrutyuchya velechya pramanapeksha khoop vegwan aahe aanee mhanunach yaa modelmadhye yaa ghatakankade durlaksh kele jaate.
yaa pratimanavar mahamari pratiman prushthavar adhik vachata yeil.
master samikaran drushtikon.
eka mukhya samikaran eka dishaheen dishaheen jaalyache vartan vyakt karoo shakate, jithe pratyek tappyavar, jaalyamadhye eka naveen node jodala jaato, joou junya nodashi jodala jaato (yadruchchikpane nivadalela aanee pradhanyashivay). prarambhik jaale done nodesdware tayar kele jaate aanee velechya sutravar tyanchyat done duve tayar kele jaatat, heey sanrachana keval pudhil ganana sulabh karnyasathi aavashyak aahe, mhanoon velechya sutravar jaalemadhye sootra _ 121 nodes aanee sootra _ 121 duve asatat.
yaa jaalyache mukhya samikaran asey aaheh
jethe sootra 124 heey vel sootra 127 varr degree sootra 27 saha node sootra 125 asanyachi sambhavyata aahe aanee sootra 125 hii networkmadhye jodali geleli vel payari aahe. lakshat ghya qee junya node sutrasathi _ 125 madhye time sootra _ 127 varr sootra _ 27 duve asane keval done marg aaheth
heey model sope kelyanantar, padvi vitaran sootra _ 138 aahe.
yaa vadhatya jaalyachya aadhare, eka sadhya niyamache palan karoon eka mahamariche model vikasit kele jaateh pratyek velee naveen node jodala jaato aanee jodanyasathi juna node nivadalyanantar nirnay ghetala jaatoh yaa naveen nodala sansarg hoil qee nahee. yaa mahamarichya pratimeche mukhya samikaran asey aaheh
jethe sootra _ 140 heey sansarg karnyacha nirnay darshavate (sootra _ 141) kinwa nahee (sootra _ 142). heey mukhya samikaran sodavtana, khaleel upay prapt hotoh sootra _ 143
bahustareey jaale.
bahustareey jaale heey anek prakarche sambandh asalele jaale aahe. samajik jaalyanche vishleshan, arthshastra, itihas, shahari aanee aantarrashtriy vahtook, paryavaranshastra, manasshastra, aushadhashastra, jivashastra, vanijya, havamanshastra, bhautikshastra, sanganakeey tantrikashastra, karya vyavasthapan aanee vitt yasarkhya vividh kshetranmadhye bahuayami jaalyanchya rupat vastavik-jaagtik pranalinche pratirup tayar karnyache prayatna kele gele aahet.
network optimization.
kahitari karnyacha ishtatam marg shodhane samavisht asalelya jaale samasyancha abhyas sanyukt optimization navakhali keela jaato. udaharananmadhye jaale pravah, sarvat lahan marg samasya, vahtook samasya, hastantaran samasya, sthan samasya, julani samasya, assignment samasya, packing samasya, marg samasya, gambhir marg vishleshan aanee part (karyakram moolyankan aanee punaravalokan tantra) yancha samavesh hoto.
parasparavalambi jaale.
parasparavalambi jaale heey jaale aahet jethe eka jaaletil nodesche karya karya jaaletil nodeschya karyavar avalambun asate. nisargat, jaale kvachitach vilgikaranat disatat, tyaeivaji, samanyatah jaale heey samanyatah mothya pranalinmadhil ghatak asatat aanee tyaa guntaguntichya pranalitil ghatkanshi sanvad sadhatat. asha guntaguntichya avalambitvamule ekmekanvar kshullak parinam houu shakatat. eka uttam abhyas kelele udaharan mhanje payabhoot suvidhanchya jaalyanche parasparavalamban, veej jaaliche kendra tayar tayar veej kendranna raste kinwa paipchya jaalyandvare indhan vitareet karane aavashyak asate aanee teey dalanvalan jaalichya kendrandware dekhil niyantrit kele jaatat. jaree vahtook jaale karya karnyasathi veej jaalevar avalambun nasale taree dalanvalan jaale teey karate. asha payabhoot suvidhanchya jaalyanmadhye, ektar veej jaalyamadhye kinwa dalanvalan jaalyamadhye mahattvapoorn sankhyene nodeschya karyat bighad jhalyamule sampoorn pranalimadhye padzad houu shakate aanee sampoorn pranalichya karyat sambhavya vinashkari parinam houu shakato. jarr done jaalyanvar vilgikaranat upchar kele gele, tarr haah mahattvacha abhipray parinam disun yenar nahee aanee jaalyachya drudhateche andaj mothya pramanat atiaadharit kele jaatil.

