Emergence of Global Network Property based on Multi-agent Voting Model

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1 Emrgn of Glol Ntwork Proprty s on Multi-gnt Voting Mol Kosuk Shino Ntionl Dfns Amy -- Hshirimizu, Yokosuk Kngw, Jpn kshino@n..jp Yutk Mtsuo Ntionl Institut of Avn Inustril Sin n Thnology -- Sotoknn, Chiyo Tokyo, Jpn y.mtsuo@ist.go.jp Hiyuki Nkshim Futur Univrsity, Hkot Hokkio, Jpn h.nkshim@fun..jp ABSTRACT Rnt stuis hv shown tht vrious mols n xplin th mrgn of omplx ntworks, suh s sl-fr n smll-worl ntworks. This ppr prsnts iffrnt mol to gnrt omplx ntworks using multi-gnt pproh. Eh no is onsir s n gnt. Bs on y ll gnts, gs r rptly. W us four iffrnt kins of ntrlity msurs s utility funtions for gnts. Dpning on th ntrlity msur, th rsultnt ntworks iffr onsirly: typilly losnss ntrlity gnrts sl-fr ntwork, gr ntrlity prous rnom grph, twnnss ntrlity fvors rgulr grph, n ignvtor ntrlity rings omplt sugrph. Th importn of th ntwork strutur mong gnts is wily not in th multi-gnt rsrh litrtur. This ppr ontriuts nw insights into th onntion twn gnts lol hvior n th glol proprty of th ntwork strutur. W sri til nlysis on why ths struturs mrg, n prsnt isussion of th possil xpnsion n pplition of th mol. Ctgoris n Sujt Dsriptors I. [Artifiil Intllign]: Distriut Artifiil Intllign Gnrl Trms Dsign, Exprimnttion. INTRODUCTION Soil ntworks r riv muh ttntion in th multignt rsrh ommunity s wll s othr rsrh omins suh s W thnology [], uiquitous thnology [] n soil sin []. Rntly, soil ntworking srvis (SNSs) hv om populr on th W. Eh usr rgistrs thir Prmission to mk igitl or hr opis of ll or prt of this work for prsonl or lssroom us is grnt without f provi tht opis r not m or istriut for profit or ommril vntg n tht opis r this noti n th full ittion on th first pg. To opy othrwis, to rpulish, to post on srvrs or to ristriut to lists, rquirs prior spifi prmission n/or f. WOODSTOCK El Pso, Txs USA Copyright X ACM X-XXXXX-XX-X/XX/XX...$.. quintns, thry mrting lrg soil ntwork. Vrious pplitions us soil ntworks,.g., informtion rommntion [] n informtion shring []. Th SNSs r onsir s multi-gnt systms: h gnt (or usr) intrts lolly, rgistring frins n quintns, xhnging informtion y writing n ommnting on wlogs (logs). Svrl stuis hv rgr soil ntwork s multi-gnt systm n propos pplitions suh s informtion rommntion [] n pulition srh []. Dspit th importn of soil ntworks for multi-gnt systms, fw stuis hv n onut into th ntur of lol hvior n glol ntwork proprtis. Som stuis hv rvl tht th ovrll prformn is mrkly influn y th ntwork strutur mong gnts [, ]. Howvr, if w xmin th pplition to soil ntwork systms suh s informtion rommntion, it is nssry to hv knowlg out how lol hvior will prou th ovrll ntwork strutur, rthr thn how th prformn iffrs pning on givn ntwork strutur. In this ppr, w propos growing ntwork mol from th multi-gnt point of viw, whih is intn to show th insight twn th lol hvior of th gnts n th rsultnt ntwork strutur. In our mol, h gnt (rogniz s no) ttmpts to inrs thir utility y ing nw gs. Th ition of n g might prfrr y som gnts, ut not y othr gnts. Rsultnt onflits mong gnts n rsolv using systm. This sitution is unrstoo n justifi y svrl soil ntwork xmpls in th rl worl: For xmpl, in lrg orgniztion, som popl slts othrs to join thir liqu, n thry strngthn it. In politil orgniztions n mi orgniztions, popl somtims try to grow thir own groups. Thy nourg othrs to mor onnt to thir group. Thrfor, it is importnt to invstigt ntwork proprtis s on n grmnt mong multipl gnts. Our prolm stting is s follows: h gnt is onsir s no. A nw g is gnrt through grmnts mong gnts, s ror through vot. Th nwly invnt g inrss th rsptiv utilitis of som gnts. This pross is itrt n th ntwork oms mor onnt. W us ntrlity msurs for utility funtions. Cntrlity, whih rprsnts how ntrl n tor is in soil ntwork, hs n long stui in th fil of soil ntwork nlysis. Espilly, w slt four ntrlity msurs, gr, losnss, twnnss n PgRnk ntrl-

2 ity, n show tht th sltion of ntrlity msur yil signifint iffrn in glol ntwork proprtis. Th ontriution of th ppr n summriz s follows: W show how lol intrtion n grmnt mong gnts onsists iffrnt ntwork proprtis. Our mol is simpl; for tht rson, w n show th si phnomnon involving lol hviors n glol proprtis. Our rsults r usful in th sign of soil ntwork srvis y multi-gnt systm, spilly in rltion to rommntions of informtion, popl, n ommunitis. W show th prliminry nlysis of n tul soil ntwork, n isuss th ppliility of our finings for rommntion systm. Th ppr is orgniz s follows. In th nxt stion, w sri rlt stuis. Thn w xplin th lgorithm of our simultion in mor til. Stion n r vot to rsults of simultion n thortil nlysis on th rsults. Stion isusss th xpnsion n ppliility of th mol, n w onlu th ppr.. RELATED WORKS Som stuis hv invstigt intrtions mong gnts n systm hvior t th olltiv lvl [, ]. Axtll shows th ffts of istint gnt intrtion n ovrll struturs in rtirmnt hvior n firm formtion. Gston monstrt tht th soil ntwork strutur unrlying n gnt orgniztion n hv onsirl impt on orgniztionl prformn. In ths stuis, ntwork mol is givn suh s ltti, rnom grph, or smll-worl grph. Although th motivtion is similr towr th importn of ntwork strutur mong gnts, th pprohs of thos stuis n ours r iffrnt, or strngthn h othr: it is importnt not only to know th rltion twn rtin ntwork strutur n th ovrll prformn, ut lso th rltion twn lol hvior n ntwork struturs. Mhnism of ntwork gnrtion suh s sl-fr or smll worl ntworks r stui in th ontxt of omplx ntworks [, ]. Th most populr xplntion of sl-fr ntworks is prfrntil tthmnt: A nwly rt no is onnt to pr-xisting on with proility proportionl to th numr of gs of th trgt no. Othr mols inlu onnting nrst-nighor mol n mutul sltion mol [], oth of whih xplin th mrgn of sl-fr ntworks. In th lttr mol, nw g is s on mutul ffinity twn nos, whih n onsir s simpl multi-gnt systm. Howvr, most stuis o not mploy th multi-gnt systm: thy o not xpliitly hv gnts ision, gols or utility funtions. A similr stuy to ours is tht of ntwork gms, whih invstigts th ynmi formtion n volution of ntworks. Jkson n Wtts propos mol [] in whih ll gnts hv th sm vlu funtion n in whih nw gs r y grmnt twn two gnts whn thy mt rnomly. Our mol is istinguish from th on in tht stuy us w mploy systm s glol grmnt mhnism; morovr, w lrify th rltion to ntwork struturs suh s sl-fr or rnom grph. Soil ntworks r importnt for vrious multi-gnt systms. In th prvious stion, w sri stuis using soil ntworks for informtion rommntions n istriut srhs [, ]. Anothr mjor pplition is trust n rputtion lultion: In th Rgrt systm propos y Str [], rputtion is lult s on soil ntwork nlyss. Pujol t l. vlop mtho to lult rputtion using only lol informtion. It n pt pt to th ntwork topology []. Ashri t l. proposs mtho to vlut th trustworthinss of gnt s ountrprts, s on n nlyss of rltionships []. Our stuy n ontriut to ths rsrh fforts y gnrting pproprit soil ntworks pning on thir intn purposs.. SIMULATION MODEL In this stion, w first ovrviw ntrlity msurs, whih r stui in soiology. Th ntrlity msur is us to rprsnt th utility of n gnt in our mol. Th ovrll stting of th simultion is xplin nxt. In our mol, nos r onsir s gnts, n gs r onsir s rltions twn gnts, whih r non-irtionl n riprol.. Cntrlity s Utility Soil ntwork nlysis inlus vrious msurs of no ntrlity tht trmin th rltiv importn of no within th ntwork []. It rprsnts th struturl importn of no, whih n prhps hrtriz s th powr of iniviul tors. Among th svrl kins of ntrlity msurs [], th most populr ons r gr, losnss, twnnss, n ignvtor ntrlity. In our mol, w ssum tht h gnt sks to inrs its ntrlity. In othr wors, ntrlity is us s proxy for utility, whih is to mximiz. Our intuition is simpl: rognizing tht tritionl stuis in soil sin hv shown th usfulnss of ntrlity s msur of powr, why not infr it s proxy for utility? In othr wors, w ssum tht n gnt hvs to inrs its powr tht n lult y ntrlity msur. In our mol, w us four kins of ntrlity msur: Dgr Th gr of no is th numr of gs to othr nos. Ators who hv mor tis to othr tors might in n vntgous positions. It is fin s Ci D = k i whr ki is th gr of no i n N N is th numr of ll nos. Closnss Closnss ntrlity pturs how los n tor is to ll th othr tors. It is lult y th minimum istn of n tor to ll othr nos. Unlik othr ntrlity msurs, th smllr th vlu is, th mor ntrl th tor. It is fin s Ci C = (L i) = P N j G ij whr Li is th vrg gosi istn of no i, n ij is th istn twn no i n j. To filitt lultion for isonnt omponnts, w st ij = N if nos i n j r isonnt. Btwnnss Th twnnss ntrlity msurs inits tht n tor is in fvor position if th tor flls on th shortst pths twn othr pirs of tors in th ntwork. It msurs th numr of ll th shortst pths tht go through th no, n is fin s th following. Ci B = P j,k N n jk(i)/n jk In tht qution,

3 [] NxtStp: slt nits rnomly. [] [] slt nits rnomly. [] [] This g wins. This g wins. Figur : Exmpl of ntwork growth. n jk nots th numr of th shortst pths twn no j n k, n n jk (i) is th numr of thos running through no i. PgRnk PgRnk [] ws propos s msur of th importn of W pg. Although PgRnk orrspons to ignvtor ntrlity (unr propr trnsformtion), w us PgRnk us of its fmilirity to omputr sin rsrhrs. It is lult itrtivly s th following. Ci P (t + ) = αa i + ( α) P j B i Cj P (t)/d j Thrin, D j is th gr of no j, B i is th numr of nighors of no i, A i is vtor rprsnting th sour of th ntwork. W st α =. n A i s uniform: h lmnt of A i is /N. This lultion is itrt until C P onvrgs.. Simultion Stting W first xplin th motivtion of our simultion mol using oupl of xmpls. Th first xmpl is highwy onstrution mong itis. Assum tht th itis initilly hv no highwys. Rsint of ithr ity woul hppy if highwy is onstrut twn two itis. Th nxt highwy might onstrut nywhr ls, ut vry ity wnts it us it improv th losnss ntrlity, i.., itizns gin onvnin. Consquntly, possil solution is tht thy i th issu through ngotition or. Svrl nits xist for th onstrution of highwy; vry ity vot for on of thm. Th winnr prforms th tul onstrution. In this mnnr, itis grully om mor onnt. A possil rsult might n mrgn of hu ity: vry itizn trvl to othr itis in short tim if thr is suh hu ity. W n tk nothr xmpl in soil ntwork in n orgniztion or group. A prson woul lik to position twn popl to thry mintin ontrol of informtion flow, i.. to inrs twnnss ntrlity. In this sitution, th rsultnt ntwork is lss likly to hv hus us popl woul ompt to hol tht ntrl position. Bs on suh intuitions, w sign our simultion in th following mnnr. Eh gnt is sprt t first. Th nit gs r slt nxt. Evry gnt hs prfrns on th ition of n g, us ition of n g woul inrs or rs th gnt s utility, i.., ntrlity msur. Eh gnt vots for th nit gs, n th g with th most vots is vntully. This rpt pross rnrs th ntwork s inrsingly onnt. In our simultion, w us th fst lgorithm to lult th twnnss []. [] []. Initiliz Assum N nos. St th numr of nits s.. Choos nits Slt no rnomly. Among th possil gs from th no, slt on rnomly s nit. Rpt until th numr of nits is, or until thr r no possil gs.. Evlut nits n vot Eh no vluts h nit using th utility funtion f. Sor th nits in rsing orr s,,...,. If multipl nits xist with th sm utility, orr thm rnomly.. A n g A n g orrsponing to th nit with th highst sor.. Trmint Trmint if th numr of gs grtr thn givn numr, or if no possil gs xists. Othrwis rpt th itrtion n go k to. Figur : Simultion prour. An illustrtion is prsnt in Figur. Initilly, w hv fiv nos n two gs, n thr nit gs whih r hosn rnomly from possil gs. Eh gnt vots for on nit. In this s, Eg otins two vots, Eg otins zro, n Eg otins thr vots. Consquntly, Eg is. Thn w hv nothr thr nits, n on of thm is going to uilt. Dtils of th simultion prour r shown in Figur. Svrl points r rquir for onsirtion: How to slt nits Thr r svrl wys to hoos nit gs. W mploy simpl on: w slt gs rnomly from th possil nw gs. W us prmtr, whih nots th numr of nits. If is lrg, th g will hosn mong mny possil gs; if is, th prour is ompltly rnom. Sor of nits Eh gnt vlut th nit using givn ntrlity msur (on of gr, losnss, twnnss, n PgRnk), n vot to thm. W ssum tht ll th gnts us th sm ntrlity to s how iffrnt ntwork woul ppr. Voting Vrious wys xist for. As mtho, w opt Bor ounting, s vis y Jn-Chrls Bor. Th mtho is us for singl-st or multiplst ltions. Bus it somtims lts roly ptl nits, th Bor ount is oftn sri s onsnsus-s ltorl systm, Eh gnt puts points to th first hoi, points to th son hoi, n point for th lst fvorl hoi. Th nit with th highst sor wins.. RESULTS AND OVERALL PROPERTY In this stion, w sri rsults of ntwork gnrtion simultion. Espilly, w xmin iffrns mong th four ntrlity msurs.

4 Figur : Ntwork growth using losnss ntrlity s utility. N=, =. Up to gs.. Closnss Cntrlity Figur shows how ntwork grows whn using losnss ntrlity s gnts utility. W st th numr of nos N to n th numr of nits to. In h ntwork, tn gs r nwly. Not tht nos r position for visuliztion. For tht rson, th position n th istn of nos imply nothing. Initilly, th ntwork hs N nos without gs. Whn w gs, svrl smll omponnts r gnrt first, whih r susquntly onnt togthr, thry rting ig isln (whn th numr of gs K is ). Th lrg omponnt grully gts lrgr onnting othr isolt nos. Finlly, ll nos r onnt (whn K=). W n s two nos with high gr. Ths r ll hus. Susquntly, nos oms grully mor irtly onnt to ithr of th two hus. Whn K=, lmost vry no is onnt through th two hus. If w rs, th g sltion oms mor rnom. It thrfor oms unlikly tht hu will mrg. If w inrs, th ntwork will show on or two hus. Figur shows th gr istriution of th gnrt ntwork. W s th powr-lw istriution in th s of losnss ntrlity (Figur ()) us it forms stright lin on logrithmi-linr plot. Chrtristilly, ths ntworks hv mg-hu, i.. no with hug gr. Figur shows som proprtis of gnrt ntworks. Rgring losnss, th hrtristi pth lngth L is th smllst mong thm. Th lustring offiint C is s low s rnom grph. As oms lrgr, L gts smllr, whih mns lrgr hu(s) pprs.. Btwnnss Cntrlity Figur shows ntwork growth using twnnss ntrlity. Initilly, th ntwork grows similrly to tht of losnss ntrlity, until th gint omponnt inlus ll th nos t K=. Aftrwr, th gs onnting two nos in smll istn r onnt. Typilly, thr pprs ntwork with gs onnting only nighors, s shown in W us spring-m mol for ntwork rwing. P(k) P(k) k () Closnss k () Dgr P(k) P(k) k () Btwnnss k () PgRnk Figur : Dgr istriution of ntwork (N=, =, k =.) Figur. Th rson is unrstoo to th following: for h gnt to inrs twnnss ntrlity, L shoul lrg. Lrg L inits long shortst pths. Consquntly, h no tns to inlu in th shortst pths. W n s tht L is lrg s shown in Tl ompr to othr ntworks. If gts lrgr, L gts lrgr too. Th gr istriution of ntwork is shown in Figur (): Most nos hv gr of ; vn th lrgst gr is smllr thn.. Dgr Cntrlity Figur illustrts th ntwork growth using gr ntrlity. Initilly, thr ppr svrl pirs of nos; thy r grully onnt. Howvr, th ntwork os not show hus or string-typ growth. Isolt nos r not sily onnt to th lrgst omponnt. Thrfor, thr r svrl isolt nos vn t K=.

5 l= l= l= Figur : Ntwork growth using twnnss ntrlity. N=, =. Up to gs. l= Tl : L n C for iffrnt vlus. ntrlity L C Closnss. (.). (.) Closnss. (.). (.) Closnss. (.). (.) Closnss mx. (.). (.) Btwnnss. (.). (.) Btwnnss. (.). (.) Btwnnss. (.). (.) Btwnnss mx. (.). (.) Dgr. (.). (.) Dgr. (.). (.) Dgr. (.). (.) Dgr mx. (.). (.) PgRnk. (.). (.) PgRnk. (.). (.) PgRnk. (.). (.) PgRnk mx. (.). (.) N =, K =. W show L n C with isolt nos n without isolt nos in th prnthss. In s of gr ntrlity, th ition of nw g ffts only th gr ntrlity of nos t oth ns. It hs no glol ffts: Eh nit g otins soli vots only from th oth ns, Othr nos will vot rnomly. Thus th rsultnt ntwork is rnom grph. Th gr istriution of ntwork is shown in Figur (). It follows Poisson istriution with mo vlu of. Tl shows tht C n L r smll, whih is lso th hrtristis of rnom grph.. PgRnk Figur illustrts th ntwork growth using PgRnk. Most nos r isolt vn if w suffiint numr of gs; Aout % of th nos r isolt t K=. Only frtion of th nos r onnt. Ths nos r highly onnt, onsisting lmost omplt grph. If w look t Tl, L is vry lrg if w inlu th isolt nos. Howvr, L within th onnt omponnts is s low s.-.. C is vry lrg ompr to othr ntworks. Th gr istriution in Figur () shows th Figur : A typil s using twnnss ntrlity. N=, =, K= (right-si) n K= (lftsi). g f Figur : Illustrtion of g ition in s of losnss ntrlity. uniform istriution on grs.. MECHANISM OF NETWORK GROWTH In this stion, w invstigt ntwork growth mor thortilly. W xplin how n why ntwork of iffrnt typs r mrg. W omit th xplntion of gr ntrlity hr us th rsultnt ntwork is rnom. For th rson, it is sy to unrstn th mhnism.. Closnss Cntrlity Th ntwork using losnss ntrlity is hrtriz y th mrgn of hus. W onsir th mhnism of th hu pprn y showing tht nwly gs strngthn th hu whn givn hu. Figur xmplifis th sitution whr hu is going to gnrt: th ntwork hs thr gs mong svn nos. No hs thr gs n is smll hu. Assum tht four gs (s shown in ott lins) r slt s

6 l= l= l= l= Figur : Ntwork growth using gr ntrlity. N =, =. Up to gs. Tl : Expt numr of vots in s of losnss. f g Sum Eg.. Eg Eg.. Eg nits. W not no tht links to hu suh s No,, s priphrl no. Ths n four g tgoris, whih n sri s follow: Eg n g whih onnts hu n n isolt no, Eg n g whih onnts two priphrl nos, Eg n g whih onnts priphrl no n n isolt no, n Eg n g whih onnts two isolt nos. Th xpt numr of vots of h nit is shown in Tl. Bus w hv four nits, h no vots points of,,, n for four gs. Th xpt vots r th vrg of th two nits if th utilitis for two nits r sm. W n s tht Eg gts th highst sor. For h priphrl no, th g onnting itslf n n isolt no is th first hoi, ut th g twn th isolt no n th hu is th son hoi. An isolt no hooss th nits tht onnt itslf to othr nos, ut hs no prfrn on othr nits. In this wy, th nit twn hu n n isolt no gts th most vots, whih mks hu mor onnt n strongr. This kin of phnomnon is visil in som rl-worl xmpls. Lt us tk n irlin ntwork for xmpl. Eh Tl : Expt numr of vots with fw nos. Sum initil (.) (.) (.) (.) (.) Eg (.) (.) (.) (.) (.) Eg (.) (.) (.) (.) (.) W show th PgRnk vlus in th prnthsis. () () () Figur : Illustrtion of g ition in s of twnnss ntrlity. irlin hs fw hu irports. Vrious ustomrs in iffrnt rgions wnt to onnt to othr itis y shortr istns: thy wnt to inrs losnss ntrlity. Thrfor, th mrgn of hus r usful in glol situtions. In similr illustrtiv xmpl, this sitution is osrv in supply hin ntwork of vrious inustris. Eh ompny prfrs short hin, thry nourging th mrgn of oupl of gint ompnis glolly. In this sitution, h no om to ovrly rly on oupl of hus too muh, prouing vulnrility ginst hu ttk, s is known to our in sl-fr ntworks,. Btwnnss Cntrlity Two phss prtin in ntwork growth whn using twnnss ntrlity: In th first phs, isolt nos r onnt until ll nos r onnt. In this phs, w n ssum two typs of g nit, s pit in Figur ();

7 l= l= l= l= Figur : Ntwork growth using PgRnk ntrlity. N =, =. Up to gs. Tl : Expt numr of vots with lrg numr of nos.... Sum initil (.) (.) (.) (.) (.) (.)... (.) Eg (.) (.) (.) (.) (.) (.)... (.) Eg (.) (.) (.) (.) (.) (.)... (.) Eg An g within th onnt omponnt, n Eg, Eg An g whih onnts onnt omponnt n n isolt no. Th formr oftn rs twnnss of th nos in th omponnt us th g will prou shortst pths with lss istns, thus smllr numr of nos r inlu in th shortst pths. Contrrily, th lttr lwys inrs twnnss us th xisting shortst pths rmin n thr will nw shortst pths. Compring Eg n Eg, Eg inrss th twnnss of No n No, whrs Eg inrss only tht of No. As rsult, Eg gts high sor of thn Eg. In this wy, ntwork lngthns n th imtr inrss (s in Figur ()). In th son phs, ll th nos r lry onnt. No ition of n g inrss twnnss, ut whih nit rss twnnss ntrlity t lst? Th st gs on tht point r thos onnting two nos with istn of two. W n s thos gs in Figur () s ott lins. In this wy, mny will pprnt in th ntwork. Whn h gnts wnt to ntrl in trms of informtion flow (s in ururti orgniztions) th ntwork tns to hv lrg L, somtims rsulting in lss ffiiny.. PgRnk Cntrlity W ssum simpl s first s in Figur to unrstn th mhnism of PgRnk ntrlity. Two g typs xist: () () Figur : Illustrtion of g ition in s of PgRnk ntrlity. Eg n g within onnt omponnt, n Eg n g whih onnts onnt omponnt n n isolt no. Eg is slt whr th isolt nos r fw, s in Figur (). Figur shows th xpt vots for Eg n Eg: Eg rivs mor vots. Howvr, in ss with numrous nos s in Figur (), th sitution is iffrnt. Eg is slt s in Figur. Eh isolt no vots for Eg us th rs of th numr of isolt nos implis th rs of PgRnk vlu. As rsult, PgRnk mks ns onnt omponnt with numrous gs; th numr of th onnt omponnt inrss vry slowly. Suh sitution is somtims osrv in rl-worl soil ntworks suh s OTAKU ommunitis in Jpn. Som gs form strong group, n othr nos pprntly rsist onntion. Th prolm is pprntly smll onntivity mong th ovrll nos.

8 . DISCUSSION Bus w sign our mol s simpl s possil, som importnt lmnts wr nglt in our mol. Thos lmnts shoul invstigt in th furthr stuis: (i) Egs r monotonously inrsing in our mol. Howvr, in rl-worl ntwork, gs n lt. Also nos n n lt. (ii) Cntrlity msurs rquir knowlg of glol ntwork topology (xpt gr ntrlity). W n hng th mol to us th go-ntri ntrlity msurs. (iii) W n mix iffrnt gnts with iffrnt ntrlity msurs n xmin th mnnr in whih th ntwork grows. Similrly, w n sign utility funtion s wight sum of svrl ntrlity msurs n osrv th rsultnt ntworks. (iv) W mploy Bor ount for, ut w might ltrntivly us ngotition mol, or som othr form to hiv grmnts mong gnts. Atully, w hv tri svrl xpnsion ut w wr unl to inlu thir sriptions in this ppr us of th sp limittion. W shll rport thos rsults in futur pprs. On pplition of our mol is th nlysis of th ntwork. W n infr whih ntrlity msur omints in n tul soil ntwork. For xmpl, w hv invstigt soil ntwork of mi rsrhrs in Jpns Soity for Artifiil Intllign (JSAI) [], n fin tht twnnss ntrlity n losnss ntrlity r two mjor ingrints with wights of. n. orrsponingly. Bs on th nlysis, w n uil rommntion systm in onfrn support systms []: h usr gnt lults th utility otin whn th usr is onnt to othr prsons. Th systm mks rommntion to oth prsons so tht thy gt quint if oth (n nighoring) gnts gr to th possil onntion. Our mol is usful in vrious soil systms tht mploy multi-gnt rhittur.. CONCLUSION W hv propos n mol of th growing ntwork. This mol inlus no in ntwork s n gnt tht vots s on utility funtion. Diffrnt ntrlity msurs ngnr iffrnt ntworks: sl-fr ntwork (losnss), rnom grph (gr), rgulr grph (twnnss), n omplt grph (PgRnk). W n us our mol in vrious kins of multi-gnt systms, spilly of soil systms. Atully, th motivtion of our rsrh lis in th vlopmnt of rommntion systms in mi onfrns. Although svrl imnsions tht rquir mor invstigtion in our mol, w liv tht this rsrh provis hlpful insights towr glol ntwork proprtis n lol ision from th multignt prsptiv.. REFERENCES [] R. Ashri, S. Rmhurn, J. Str, M. Luk, n N. Jnnings. Trust vlution through rltionship nlysis. In Pro. AAMAS,. [] R. Axtll. Effts of Intrtion Topology n Ativtion Rgim in Svrl Multi-Agnt Systms, pgs. Springr,. From our xprin, without suh mhnism, h usr gnt simply rommns onntion to uthorittiv prsons, whih is not pproprit for th ommunity. [] A.-L. Brási. LINKED: Th Nw Sin of Ntworks. Prsus Pulishing, Cmri, MA,. [] A. Birukou, E. Blnziri, n P. Giorgini. Multi-gnt systm tht filitts sintifi pulitions srh. In Pro. AAMAS,. [] U. Brns. A fstr lgorithm for twnnss ntrlity. Journl of Mthmtil Soiology, ():,. [] S. Brin n L. Pg. Th ntomy of lrg-sl hyprtxtul w srh ngin. In Pro. th WWW Conf.,. [] L. C. Frmn. Cntrlity in soil ntworks: Conptul lrifition. Soil Ntworks, :,. [] M. G. Gston. Agnt-orgniz ntworks for ynmi tm formtion. In Pro. AAMAS,. [] T. Hop, M. Hmski, Y. Mtsuo, n T. Nishimur. Strngthning ommunity with moi soil ntworks. In Pro. HCI,. [] M. Jkson n A. Wtts. Th volution of soil n onomi ntworks. Journl of Eonomi Thory, :,. [] Y. Mtsuo, J. Mori, M. Hmski, H. Tk, T. Nishimur, K. Hsi, n M. Ishizuk. POLYPHONET: An vn soil ntwork xtrtion systm. In Pro. WWW,. [] J. Mori, M. Ishizuk, T. Sugiym, n Y. Mtsuo. Rl-worl orint informtion shring using soil ntworks. In Pro. ACM GROUP,. [] W. Njl, S. Ghit, n R. Piu. Smntilly rih rommntions in soil ntworks for shring, xhnging n rnking smnti ontxt. In Pro. ISWC,. [] A. S. Pntln. Soilly wr omputtion n ommunition. IEEE Computr,. [] J. Pujol, R. Sngüs, n J. Dlgo. Extrting rputtion in multi gnt systms y mns of soil ntwork topology. In Pro. AAMAS,. [] J. Str n C. Sirr. Rputtion n soil ntwork nlysis in multi-gnt systms. In Pro. AAMAS,. [] S. St, P. Domingos, P. Mik, J. Golk, L. Ding, T. Finin, A. Joshi, A. Nowk, n R. Vllhr. Soil ntworks ppli. IEEE Intllignt Systms, pgs,. [] W. Wng, B. Hu, T. Zhou, B. Wng, n Y. Xi. Mutul sltion mol for wight ntworks. Physil Rviw E,,. [] S. Wssrmn n K. Fust. Soil ntwork nlysis. Mthos n Applitions. Cmrig Univrsity Prss, Cmrig,. [] D. Wtts. Six Dgrs: Th Sin of Connt Ag. W. W. Norton & Compny,. [] B. Wllmn. Th glol villg: Intrnt n ommunity. Th Arts & Sin Rviw, Univrsity of Toronto, ():,. [] J. Wng, C. Mio, n A. Goh. Trust-s gnt ommunity for ollortiv rommntion. In Pro. AAMAS,.