A genetic search of patterns of behaviour in OSS communities

A gene ic sea ch o pa e ns o beha iou in OSS communi ies M.R. Ma ínez-To es ⇑ Uni e si y o Se ille, Facul ad de Tu ismo y Finanzas, A da. San F ancisco Ja ie , s/n 41018 Se illa, Spain a icle in o Keywo ds: Open sou ce so wa e Vi ual communi ies Social ne wo k analysis Gene ic algo i hm Fac o analysis abs ac This pape p oposes he iden ifica ion o pa e ns o beha iou o open sou ce so wa e (OSS) communi- ies using ac o analysis and hei social ne wo k analysis (SNA) ea u es. OSS communi ies can be modelled as a social ne wo k in which nodes ep esen he communi y membe s and a cs ep esen he social in e ac ions among hem, and ac o analysis is able o p o ide he ac o s ha explain he la en pa e ns o beha iou . Due o he complexi y o he p oblem and he high numbe o SNA ea u es ha can be ex ac ed, his pape p oposes a gene ic sea ch o an op imum subse o indica o s leading o a g oup o la en pa e ns o beha iou maximizing he explained da a a iance and he in e p e a ion o ac o s. Ob ained esul s illus a e he easibili y o he p oposed amewo k o ex ac ele an in o ma- ion om a la ge se o da a. Ó2012 Else ie L d. All igh s ese ed. 1. In oduc ion The OSS p ojec s di e g ea ly om comme cial so wa e de el- opmen models in se e al aspec s. Fo ins ance, comme cial so - wa e companies p e en access o he sou ce code o hei p oduc s om ou side de elope s and cus ome s, while OSS allows sou ce code o be eely modified and edis ibu ed unde ‘‘open sou ce’’ licenses (Felle & Fi zge ald, 2002). Besides, OSS p ojec s a e ypically de eloped in a dis ibu ed and decen alized way as a di e ence o p op ie a y so wa e, based on closed and o mal s uc u es. P ecisely, one o he mos dis inc i e cha ac e is ics o OSS p ojec s is he ac ha hey a e w i en, de eloped, and de- bugged la gely by wo ldwide olun ee s, who in mos cases a e connec ed and collabo a e solely h ough he In e ne . The e o e, he communi y behind he de elopmen o he p ojec plays an essen ial ole o he p ojec o success (Deek & McHugh, 2008). Se e al au ho s ha e desc ibed OSS de elopmen eams as ha - ing a hie a chical o onion-like s uc u e (C ows on & Howison, 2005), wi h a cen al co e o highly ac i e indi iduals, su ounded by o he laye s o p og essi ely less ac i e indi iduals. One exam- ple o his is p esen ed in he s udy by Ye, Nakakoji, e al. (2005) whe e he cen al co e is composed o he p ojec leade s and co e membe s, wi h fi e ou e laye s con aining ac i e de elope s, pe iphe al de elope s, bug epo e s, passi e use s, and s akehold- e s, espec i ely. I has been demons a ed ha much o he OSS de elopmen is ealized by a small pe cen age o indi iduals de- spi e he ac ha he e a e ens o housands o a ailable de elop- e s. Such concen a ion is called ‘‘pa icipa ion inequali y’’ (Kuk, 2006), and i can be explained by he di e en use p ofiles o open sou ce communi ies. Pa icipa ion inequali y allows he ca ego i- za ion o OSS communi y membe s in h ee g oups (Mockus, Fielding, & He bsleb, 2002; Xu, Gao, Ch is ley, & Madey, 2005). Co e membe s a e esponsible o guiding and coo dina ing he de elopmen o an OSS p ojec . They a e usually in ol ed wi h he p ojec du ing a long pe iod o ime and ha e made significan con ibu ions o he de elopmen and e olu ion o he sys em. Mode a o s and leade s a e included in his g oup. Ac i e de elop- e s a e hose communi y membe s ha egula ly make con ibu- ions o he p ojec . Finally, pe iphe al de elope s occasionally con ibu e wi h new ea u es o he exis ing sys em. This con ibu- ion is i egula , and he pe iod o in ol emen is sho and spo- adic. F ee ide s (people who jus a e seeking answe s wi hou making any con ibu ions) a e also included in his g oup. The social s uc u e o OSS eams di ec ly influences he pa icipa ion and he decision-making p ocess a ec ing he o e all pe o mance o he p ojec . The e o e, an impo an esea ch ques ion is ex ac ing he di e en pa e ns o beha iou in OSS communi ies. These pa e ns leading o success ul p ojec s a e o g ea in e es bo h o au onomous and sponso ed communi ies, ha sha e a common aim o e aining and a ac ing pa icipan s o hei communi ies (Wes & O’mahony, 2008). Howe e , he s uc u e o communi ies can only be de i ed om he pa icipa- ion ac i i y o hei membe s. Fo his pu pose, OSS communi ies ha e been equen ly modelled as a social ne wo k, being he nodes o he ne wo k he communi y membe s while he a cs ep esen he flow o in e ac ions among use s (To al, Ma ínez-To es, & Ba e o, 2009a). These ne wo ks a e hen analyzed using Social Ne wo k Analysis (SNA) echniques by ob aining a se o SNA ea- u es. Fo ins ance, p e ious s udies ha e conside ed he size and ou -deg ee o nodes (Val e de, The aulaz, Gau ais, Fou cassie, & 0957-4174/$ - see on ma e Ó2012 Else ie L d. All igh s ese ed. h p://dx.doi.o g/10.1016/j.eswa.2012.05.083 ⇑ Tel.: +34 954 55 43 10; ax: +34 954 55 69 89. E-mail add ess: [email p o ec ed] Expe Sys ems wi h Applica ions 39 (2012) 13182–13192 Con en s lis s a ailable a SciVe se ScienceDi ec Expe Sys ems wi h Applica ions jou nal homepage: www.else ie .com/loca e/eswa Sole, 2006), closeness cen ali y (Panchal, 2009) and be weeness cen ali y (Hossain, Wu, & Chung, 2006; To al, Ma ínez-To es, Ba e o, & Co és, 2009b), he clus e ing coe ficien (Kwon, Oh, & Jeon, 2007; Singh, 2010), s uc u al holes (Okoli & Oh, 2007)o he b oke age ole o nodes (Sowe, S amelos, & Angelis, 2006; Ba cellini, Dé ienne, & Bu kha d , 2009; To al, Ma ínez To es, & Ba e o, 2010), among o he SNA ea u es. Mo eo e , each o hese measu emen s can be compu ed o he whole ne wo k o o se e al specific sub-ne wo ks like he one ob ained om ac i e de elope s o om he co e g oup o he communi y. Due o he la ge numbe o possible SNA indica o s ha can be ob ained, p e ious s udies ha e been ocused on a small numbe o social ne - wo k ea u es o cha ac e ize pa icipa ion and ob ain OSS pa e ns o beha iou . As a di e ence, in his s udy pa icipa ion is analyzed using he whole se o SNA ea u es ha can be ob ained om OSS communi ies. Fo his pu pose, a gene ic sea ch o he op imum subse o indica o s able o p o iding he main pa e n o beha iou in OSS communi ies is p oposed. The e o e, he main con ibu ion o his pape is he possibili y o dealing wi h all he SNA ea u es o he social ne wo ks modelling OSS communi ies h ough an e olu iona y compu a ion echnique like Gene ic Algo i hms. The emainde o he pape is s uc u ed as ollows. Fi s , p e i- ous s udies ela ed o social ne wo k s uc u es in OSS communi ies a e e iewed in Sec ion 2. In Sec ion 3 he p oblem is o mula ed and he p oposed app oach desc ibed. Sec ion 4desc ibes he Gene ic Algo i hm implemen a ion. Ob ained esul s and discus- sion a e included in Sec ion 5. Finally, conclusions a e de ailed in Sec ion 6. 2. Rela ed wo k Social ne wo k heo y is based on he idea ha social in e ac- ion pa e ns eflec he beha iou o indi iduals (F eeman, 2004). The e o e, he analysis o he social in e ac ions can p o ide in o ma ion abou how indi iduals beha e o how g oups a e o ga- nized. This is why social ne wo k analysis ocuses on he ela ion- ships be ween people, ins ead o on cha ac e is ics o people. By mapping hese ela ionships, ne wo k analysis helps o unco e he eme gen and in o mal communica ion pa e ns p esen in an o ganiza ion, which in u n can be used o explain se e al o ga- niza ional phenomena. A social ne wo k can be modelled as a g aph wi h nodes ep e- sen ing people o g oups, and links ep esen ing ela ionships o in o ma ion flows be ween hem. OSS communi ies cons i u e clea examples o dynamic social ne wo ks, as i is changing o e ime. Social ne wo ks begin when de elope s join a p ojec , wo k wi h o he s, and o m co-wo king ela ionships (Xu, Ch is ley, & Madey, 2006). These ela ionships a e impo an because he sense o belonging o a g oup is encou aged h ough social ne wo k bonding. The aim o OSS communi ies is a ac ing and e aining people, as his will benefi he unde lying so wa e. As new mem- be s join he communi y, di e en use p ofiles eme ge. No all he use s a e in e es ed in pa icipa ing he same way. Some o hem, a small pe cen age, in ensely con ibu e o he de elopmen o he p ojec , while he es o hem make egula , occasional o e en no con ibu ion a all. These a ie y o use p ofiles lead o a co e/pe iphe y s uc u e, whe e he co e g oup o de elope s is lo- ca ed a he cen e o he communi y and he es o hem a away om he cen e depending on hei con ibu ions. The co e g oup membe s a e s ongly connec ed o each o he while he pe iphe y con ains membe s who a e usually weakly connec ed o each o he as well as o he co e membe s (Long & Siau, 2007). Ma hema ically, a social ne wo k can be ep esen ed as a g aph G=(V, E) whe e Vdeno es a fini e se o e ices and E deno es a fini e se o edges such ha E#VV. Some ne wo k analysis me hods a e easie o unde s and when g aphs a e concep ualized as ma ices (Nooy, M a , & Ba agelj, 2005) as shown in Eq. (1). M¼ðm i;j Þ n  n ;whe e n¼jVj;m i;j ¼1i ð i ; j Þ2E 0 o he wise ð1Þ In case o a alued g aph, eal alued weigh unc ion w(e)is defined on he se o edges, i.e., wðeÞ¼ExR, and he ma ix is hen defined as gi en by Eq. (2). M i;j ¼wðeÞi ð i ; j Þ2E 0 o he wise ð2Þ In he con ex o OSS communi ies, V is gi en by all he commu- ni y membe s and E is gi en by he in e ac ions among hem. The esul ing ne wo k is a di ec ed ne wo k in he sense ha edges a e ac ually a cs om one communi y membe o ano he one, and he di ec ion o he a cs shows he flow o in o ma ion be ween hem. I is also a alued ne wo k, as i is possible mul iple in e ac ion be- ween he same communi y membe s. Ne wo ks can be pa i ioned using some disc e e cha ac e is ics o e ices. Fo ins ance, se e al classes o e ices can be ob ained using he unc ion w(e), ha is, he s eng h o a cs. In he case o OSS p ojec s, hese kinds o pa i ions should highligh he co e/ pe iphe y (C/P) s uc u e o he communi y. A C/P s uc u e di ides e ices in h ee dis inc subg oups: e ices in he co e, densely connec ed wi h each o he , and e ices on he pe iphe y, which in u n can be di ided in ac i e and pe iphe al e ices depending on hei le el o in e ac ion. The ollowing lis summa izes he cha ac e is ics ha can be compu ed o he whole ne wo k o each o he men ioned sub- ne wo ks as well as he main p e ious s udies ocused on hem. Size and connec i i y: he size o he communi y is he numbe o membe s he communi y has and he numbe o a cs ep esen he connec i i y among hese communi y membe s. Bo h indica- o s has been equen ly used as a measu e o he success ul de el- opmen o a OSS p ojec . Success in a i ual communi y could be mani es ed h ough he le el o pa icipa ion, which can be unde - s ood as he numbe o pa icipan s (P eece, 2001) o as he le el o communi y ac i i y and quan i y o communi y wo k ou pu (Hinds & Lee, 2008). Se e al opological indices based on connec- i i y can be compu ed, like he Zag eb g oup index, he Randic connec i i y index o he Pla index, all o hem defined in e ms o connec ions o nodes (De ille s & Balaban, 1999). Densi y: i is defined as he numbe o lines in a simple ne wo k, exp essed as a p opo ion o he maximum possible numbe o lines. The main p oblem o his defini ion is ha i does no ake in o accoun alued lines highe han 1 and i depends on he ne - wo k size. A di e en measu e o densi y is based on he idea o he deg ee o a node, which is he numbe o lines inciden wi h i (To - al e al., 2009a). A highe deg ee o nodes yields a dense ne wo k, because nodes en e ain mo e ies. The ad an age o a e age de- g ee is ha i is a non-size dependen measu e o densi y. As OSS communi ies a e di ec ed ne wo ks, se e al s a is ical measu es o he ou -deg ee dis ibu ion can be conside ed. Finally, densi y can be measu ed al e na i ely using an egocen ic poin o iew; he egocen ic densi y o a node is he densi y o ies among i s neighbou s (Nooy e al., 2005). In p e ious wo ks, densi y has been used o s udy he coo dina ion pe o mance o OSS p ojec s. Se - e al s udies conclude he e is a nega i e impac o densi y o e he quali y o he p ojec and i s coo dina ion (Hossain & Zhu, 2009; Feczak & Hossain, 2011). Componen s: A s ong componen is a maximal s ongly con- nec ed subne wo k. A ne wo k is said o be s ongly connec ed i each pai o e ices is connec ed by a pa h, aking in o accoun he di ec ion o a cs (Nooy e al., 2005). In he con ex o his s udy, M.R. Ma ínez-To es / Expe Sys ems wi h Applica ions 39 (2012) 13182–13192 13183 componen s allow he iden ifica ion o connec ed subs uc u es in he OSS communi y. K-co es:ak-co e is a sub-ne wo k in which each node has kde- g ee in ha sub-ne wo k. The co e wi h he highes deg ee is he cen al co e o he ne wo k, de ec ing he se o nodes whe e he ne wo k es s on (To al e al., 2010). Dis ance: i is defined as he numbe o s eps in he sho es pa h ha connec s wo e ices. Dis ance be ween membe s in he OSS communi y can a ec how ideas and discussions can sp ead o e he communi y. Sho dis ances mean in o ma ion only has o a el a ew links o each anybody in he ne wo k (Xu e al., 2006). Closeness cen aliza ion: i is an index o cen ali y based on he concep o dis ance. The closeness cen ali y o a node is calcula ed conside ing he o al dis ance be ween one node and all o he nodes, whe e la ge dis ances yield lowe closeness cen ali y sco es. The closeness cen aliza ion is an index defined o he whole ne wo k, and i is calcula ed as he a ia ion in he closeness cen ali y o e ices di ided by he maximum a ia ion in close- ness cen ali y sco es possible in a ne wo k o he same size (To al e al., 2009b). I has been ound ha closeness cen aliza ion has a posi i e co ela ion wi h coo dina ion mechanism on OSS p ojec s (Pe ei a & Soa es, 2007; Feczak & Hossain, 2011). Be weenness cen ali y: i is a measu e o cen ali y ha es s on he idea ha a pe son is mo e cen al i he o she is mo e impo an as an in e media y in he communica ion ne wo k (Nooy e al., 2005). The cen ali y o a node depends on he ex en o which his node is needed as a link o acili a e he connec ion o nodes wi hin he ne wo k. I a geodesic is defined as he sho es pa h be ween wo nodes, he be weenness cen ali y o a e ex is he p opo ion o all geodesics be ween pai s o o he e ices ha include his e ex, and be weenness cen aliza ion o he ne wo k is he a i- a ion in he be weenness cen ali y o e ices di ided by he max- imum a ia ion in be weenness cen ali y sco es possible in a ne wo k o he same size. I has been used o s udy he hie a chy and cen aliza ion in ee and open sou ce so wa e eam commu- nica ions (C ows on & Howison, 2006). B oke age oles: A b oke is a middle node in a di ec ed iad (a se o h ee e ices and he lines among hem). Di e en ypes o b oke age oles can be dis inguished conside ing media ion be- ween membe s o he same o di e en g oups. In his con ex o OSS communi ies, hese g oups a e gi en by ac i e and pe iph- e al membe s. The e o e, wo possibili ies o media ion can be con- side ed as shown in Fig. 1. The ole o knowledge b oke s has been highligh ed in mailing lis s as communi y acili a o s, helping answe hose ques ions knowledge seeke s pos ed (Sowe e al., 2006). This ole has also been assigned o he co e eam o he OSS p ojec , ac ing as in e - media y be ween expe so wa e de elope s and pe iphe al use s and helping OSS p ojec s o engage in a discou se and co-lea ning expe ience wi h hei use communi ies (To al e al., 2010). Clus e ing coe ficien : I measu es whe he fi s deg ee neigh- bou s o a pa icula e ex in e ac wi h each o he . Basically, clus e ing coe ficien is a measu e o local cohesi eness h ough he neighbou in e ac ions o a e ex (Du ugbo, 2012). The clus- e ing coe ficien o a e ex is defined as he a io o he numbe o links o he o al possible numbe o links among i s neighbou s, and he clus e ing coe ficien o a social ne wo k is he a e age o all he clus e ing coe ficien s o he e ices. I has been used o cha ac e ize he small-wo ld phenomena in ne wo ks (Xu e al., 2006). Besides, highly clus e ed ne wo ks p o ide be e in o ma- ion p opaga ion (Gao & Madey, 2007). P oximi y p es ige: I is defined in e ms o he ou pu domain o a node, which is he numbe o nodes o which he e is a pa h o ha node. Following Nooy e al. (2005) defini ion, he p oximi y p es ige o a node is he p opo ion o all nodes in he ne wo k (excluding i sel ) ha a e in i s ou pu domain di ided by he mean dis ance om all nodes in i s ou pu domain. The e o e, a ze o a- lue o he p oximi y p es ige means ha his node is isola ed. 3. Fo mula ion o he p oblem and p oposed amewo k The p oblem consis s o finding a se o SNA indica o s able o explain he di e en s uc u al pa e ns o OSS communi ies. Fac- o Analysis is a mul i a ia e s a is ical echnique usually em- ployed o he iden ifica ion o la en dimensions o ac o s on a da ase . These ac o s a e no di ec ly obse able and segmen he da ase in o ela i ely homogeneous segmen s (Renche , 2002). I is assumed each a iable is dependen on a linea combi- na ion o he common ac o s, and he coe ficien s a e known as loadings (To al & Ma ínez To es, 2009c). Ma hema ically, he ac- o analysis model exp esses each a iable as a linea combina ion o unde lying common ac o s 1 , 2 ,... , m , wi h an accompanying e o e m o accoun o ha pa o he a iable ha is unique (no in common wi h he o he a iables). Fo y 1 ,y 2 ,... ,y p in any obse a ion ec o y, he model is as ollows: y 1  l 1 ¼k 11 1 þk 12 2 þþk 1m m þ e 1 y 2  l 2 ¼k 21 1 þk 22 2 þþk 2m m þ e 2 ... y p  l p ¼k p1 1 þk p2 2 þþk pm m þ e p ð3Þ Model (3) can be w i en in ma ix no a ion as in Eq. (4), whe e K is he ac o loadings ma ix. y l ¼ K þ e ð4Þ The coe ficien s k ij a e called loadings and se e as weigh s, showing how each y i indi idually depends on he unde lying ac- o s (Lee and Lee, 2011). Wi h app op ia e assump ions, k ij indi- ca es he impo ance o he j h ac o j o he i h a iable y i and can be used in in e p e a ion o j . I is expec ed he loadings will pa i ion he a iables in o g oups co esponding o ac o s. Ideally, he numbe o ac o s mshould be subs an ially smalle han he p oblem dimension p; o he wise we ha e no achie ed a pa simonious desc ip ion o he a iables as unc ions o a ew unde lying ac o s. In he case o explo a o y ac o analysis, he lack o heo e ical backg ound causes ha he numbe o ac o s o be ex ac ed is a p io i unknown. The e o e, ac o s mus be se- lec ed a ending o he homogenei y o hei indica o s. The main p oblem o using ac o analysis when conside ing a la ge se o indica o s is ha he final esul is condi ioned by he numbe o a iables included in he analysis. The desc ibed model y o fi he da a in se o ac o s, and he inclusion o non app op ia e a iables may dis o he ob ained la en ac o s. Howe e , i is no easy o decide which a iables a e o no app o- p ia e, abo e all in hose si ua ions whe e he heo e ical back- g ound canno guide his p ocess. This pape p oposes a compu a ion amewo k whe e he selec ion o indica o s is pe - o med using Gene ic Algo i hms (GA). Each elemen (o ch omo- some using ypical GA no a ion) o he popula ion conside ed by GA ep esen a subse o all he possible SNA indica o s. Fig. 2 shows a b ie scheme o he p oposed amewo k. B oke B oke Ac i e membe Pe iphe al membe Ac i e membe Pe iphe al membe Fig. 1. B oke age oles. 13184 M.R. Ma ínez-To es / Expe Sys ems wi h Applica ions 39 (2012) 13182–13192 The de eloped algo i hm consis s o wo loops. The inne loop consis s o he e alua ion o he fi ness unc ion o each elemen o he popula ion using ac o analysis. The ou e loop gene a es a new gene a ion using gene ic ope a o s like ep oduc ion, c oss- o e and mu a ion, using a selec ion based on he indi idual fi ness o each elemen o he popula ion. The amewo k s ops wo king when a selec ed s opping c i e ion is eached. 4. Gene ic algo i hm implemen a ion Gene ic Algo i hms a e a amily o compu a ional models in- spi ed by e olu ion (Holland, 1975; Goldbe g, 1989). These algo- i hms encode a po en ial solu ion o specific p oblem on a simple ch omosome-like da a s uc u e and apply gene ic ope a- o s o hese s uc u es in o de o p ese e c i ical in o ma ion (Ma ínez-To es & To al-Ma ín, 2010). An ini ial popula ion Pi composed o N ch omosomes is conside ed. Goldbe g (1989) s ud- ied he op imum numbe o ch omosomes o a popula ion acco d- ing o he ch omosome’s leng h. His main conclusion was ha he op imum popula ion’s size alue ge s highe as he ch omosome’s leng h inc eases. This ini ial popula ion is gene a ed andomly in o de o p ese e he di e si y in he popula ion and he fi ness unc ion is calcula ed o e alua e he goodness o each ch omo- some. The mechanism o gene a ing he subsequen gene a ions is based on he selec ion scheme om ( l +k) e olu ion s a egy (Michalewicz, 1996;Reina, To al, Johnson, & Ba e o, 2012). The l bes ch omosomes a e included di ec ly in he nex gene a ion. The c osso e and mu a ion ope a ions a e esponsible o gene a - ing kch omosomes o a new popula ion. The c osso e consis s o using wo membe s o a popula ion P j o gene a e wo new mem- be s o he nex popula ion P j+1 by c ossing hei gene ic in o ma- ion. The new ch omosomes con ain gene ic in o ma ion om he p edecesso s. The pu pose o mu a ion is o change he gene ic in o ma ion o a ch omosome included in P j o gene a e a new ch omosome o P j+1 .Fig. 3 illus a es he implemen ed gene ic algo i hm. 4.1. Ch omosome encoding A ch omosome C i ep esen he subse o indica o s ha will be conside ed o pe o m ac o analysis. The o al numbe o Fig. 2. P oposed amewo k. Fig. 3. Ou line o he gene ic algo i hm implemen a ion. M.R. Ma ínez-To es / Expe Sys ems wi h Applica ions 39 (2012) 13182–13192 13185 indica o s ex ac ed o he OSS communi ies acco ding o he de- sc ibed SNA ea u es is 60 (see appendix). The e o e, each ch omo- some is a bina y s ing o leng h 60 whe e a alue o 1 means ha he co esponding a iable is pa o he conside ed subse o indica o s and a alue o 0 means ha i is excluded om his lis . No ice ha he space o possible solu ions is o med by 2 60 = 1.1529e+018 possibili ies. Tha means ha we should pe - o m 2 60 di e en ac o analyses o comple ely explo e he space o possible solu ions. In his kind o p oblems, GA can pe o m a guided sea ch o he op imum solu ion wi h lowe compu a ional cos han explo ing one by one all he possibili ies. The ep esen a- ion o ch omosomes as bina y s ings has he ad an age ha his ch omosomal encoding is comple e and alid. Comple e means ha he whole space o possible solu ions can be ep esen ed and alid means ha all o hem can be compu ed. The composi- ion o a ch omosome is shown in Fig. 4. 4.2. E alua ion unc ion The fi ness unc ion quan ifies he sui abili y o each ch omo- some as a solu ion. Gene ic ope a o s make selec ions based on indi idual fi ness. Tha means ha ch omosomes wi h high fi ness alue ha e mo e chance o being selec ed, passing hei gene ic ma e ial ( ia ep oduc ion, c osso e o mu a ion) o he nex gen- e a ion. As a esul , he fi ness unc ion p o ides he p essu e o e olu ion owa ds a new gene a ion wi h ch omosomes o highe fi ness han he p e ious ones. In his case, he fi ness unc ion should measu e how well ac o analysis can iden i y la en ac o s. Howe e , i s capaci y o pe o m such iden ifica ion depends on he ollowing pa ame e s: Explained a iance: I e e s o he pe cen age o he o al sam- ple a iance explained by he conside ed ac o s. Co ela ions be ween a iables: I is he a e age o he sum o he squa ed co ela ion coe ficien s be ween indica o s. Consid- e ed indica o s mus be co ela ed as he ac o analysis is based on he in e ela ionships among a iables. In e p e abili y o ac o s: A ac o is well defined i i is explained by a leas h ee a iables (Renche , 2002). Tha is o say, a leas h ee di e en ac o loadings should be maxi- mized o each conside ed ac o . As a esul , he fi ness unc ion equi es o be defined as a mul- i-objec i e fi ness unc ion conside ing he a o emen ioned pa ame e s. F¼c 1 Va þc 2 1 nX k i¼1 2 i þc 3 In e p ð5Þ Explained a iance and co ela ions among a iables exe opposi e e ec s on he e olu ion o GA. Explained a iance makes he GA o e ol e owa ds a minimum numbe o indica o s, as i is easies o explain he a iance o he da ase whene e a lowe numbe o a iables a e conside ed. As a di e ence, co ela ions among a iables makes he GA o sea ch o a highe numbe o a iables, as his pa ame e is maximized by including as many a iables as possible. Howe e , he hi d pa ame e , in e p e abil- i y o ac o s, is he mos impo an one, because his pa ame e gua an ees ac o s a e well defined. C 1 ,C 2 , and C 3 coe ficien s in Eq. (5) a e used o adjus he ela- i e impo ance o he h ee pa s o he fi ness unc ion. Ob i- ously, he ange o hem is [0,1], wi h he es ic ion o C 1 +C 2 +C 3 =1. 4.3. S opping c i e ia The popula ion’s a e age fi ness unc ion has been chosen as he s op c i e ion o he gene ic algo i hm. I P a ,j deno es he pop- ula ion’s a e age fi ness unc ion, he s opping c i e ion can be o - mula ed as: S c !P a ;jþ1 P a ;j ð6Þ 4.4. P ocedu e o ansi ion The p ocedu e used o gene a e a new popula ion P j+1 om he p e ious popula ion P j is as ollows: The bes 20% ch omosomes a e copied om P j o P j+1 . This ensu es ha he bes indi iduals o each popula ion will be included in he nex gene a ion. As a consequence, he likeli- hood o using a good ch omosome o ep oduc ion ope a ions ge s highe . The 80% o he new ch omosomes a e gene a ed by using c oss- o e (75%) and mu a ion (5%) ope a ions. This aims o a ou he di e si y o he ch omosomes. P c deno es he p obabili y o a ch omosome C i o ake pa in a c osso e ope a ion and i is calcula ed as: P Ci ¼ ðC i Þ P n i¼1 ðC i Þð7Þ The e m (C i ) s ands o he e alua ion o he fi ness unc ion o he ch omosome C i . Consequen ly, he bes ch omosomes a e mo e likely o be selec ed. The c osso e ope a ion is illus a ed in Fig. 5. A one-poin c osso e ope a ion has been implemen ed. The poin o c oss is deno ed by p k , whe e 0 6k6l, and lis he size o he ch omosome. The alue o kis andomly chosen o each c osso e ope a ion. This poin di ides each ch omosome in o wo pa s RG j and LG j . The wo new ch omosomes a e hen ob- ained swapping LG j,1 by LG j,2 . Simila ly, P m is he p obabili y o a ch omosome i o ake pa in a mu a ion ope a ion. The pu pose o mu a ion is o make small changes in he ch omosomes. These changes consis o modi ying one ch omosome’s bi . Acco ding o De Jong (1975) we ha e calcu- la ed P m as l 1 . The mu a ion ope a ion is illus a ed in Fig. 6. The posi ion o he mu a ed bi is deno ed by p m , whe e 06m6l. The alue o p m is andomly chosen o each mu a ion ope a ion. 5. Resul s The p oposed app oach has been applied o wel e i ual communi ies lis ed in Table 1. They co espond o Linux Debian po s o di e en p ocesso a chi ec u es. The Debian P ojec is an associa ion o indi iduals who ha e made common cause o c ea e a ee ope a ing sys em called Debian GNU/Linux, o simply Debian o sho (Robles, Gonzalez-Ba ahona, & Michlmay , 2005; Ma eos-Ga cia & S einmuelle , 2008). Each communi y was analyzed om he yea in which each communi y s a ed i s ac i i y o 2010. Fo each yea and commu- ni y, a social ne wo k based on in e ac ions among pa icipan s has been ex ac ed. As a esul , a o al o 134 social ne wo ks ha e been analyzed, ex ac ing he se o da a de ailed in he appendix. 1 I1 0 I2 1 I3 0 I4 1 I5 0 I6 . . . 1 I59 0 I60 Fig. 4. Ch omosome’s composi ion. 13186 M.R. Ma ínez-To es / Expe Sys ems wi h Applica ions 39 (2012) 13182–13192 Once his la ge da ase has been ob ained, GA has been applied o ob ain an op imum subse o indica o s able o iden i y OSS commu- ni ies p ofiles acco ding o hei opological pa icipa ion s uc u e. A popula ion’s size o 10000 ch omosomes will be conside ed (Alande , 1992). Tha means ha he 2000 bes ch omosomes a e di- ec ly included in he nex popula ion, 7500 ch omosomes a e gen- e a ed by he c osso e ope a ion and 500 ch omosomes a e gene a edby hemu a ionope a ion.Fac o analysisis used o e al- ua ing each ch omosome. The cos unc ion ollows he gene al s uc u e defined in Eq. (5). The coe ficien s C 1 ,C 2 and C 3 ep esen he ela i e weigh o each pa o he fi ness unc ion. GA has been un o di e en alues o he h ee pa ame e s, ob aining he esul s shown in Table 2. I can be obse ed ha in e p e abili y only eaches a alue o 1 when C 3 is o e weighed, while he explained a iance a ies depending on he alue o C 1 . Tha is why he se o coe ficien s wi h he alues C 1 = 0.1, C 2 = 0.1 and C 3 = 0.8 has been chosen (This se o alue is shown in i alics in Table 2). An in e p e - abili y o ac o s equal o 1 gua an ees ha all he la en ac o s a e in e p e able. Using his se o alues, GA con e ged a e 30 gene - a ions, wi h an explained a iance o 70.93%, and 23 indica o s g ouped in ou ac o s. Time equi ed by gene ic algo i hm execu- ion was 2873.6 s (47.89 min). This alue is much smalle han he al e na i e op ion o explo ing he whole solu ion space. Acco ding o he chosen encoding, he size o a ch omosome is l=60bi s, so he space o possible solu ions is 2 l =2 60 = 1.1529e+018. The idea o finding he op imum solu ion explo ing all he possibili ies is una - ainable. The ime necessa y o ca y ou a single ac o analysis is 12.9 ms.Tha means i would ake mo e han 470 millionyea s o ex- plo e he whole space o possible solu ions. The gene ic algo i hm implemen a ion is able o speed up he sea ch o an op imal solu ion. Fig. 5. C osso e ope a ion. Fig. 6. Mu a ion ope a ion. Table 1 Analyzed Linux Debian communi ies. URL Desc ip ion Pe iod Debian po o m68k (Debian-68k) h p://lis s.debian.o g/debian-68k/ Mo o ola 68k po o Debian GNU/Linux. Debian cu en ly uns on he 68020, 68030, 68040 and 68060 p ocesso s 1998–2010 Debian po o ARM (Debian-ARM) h p://lis s.debian.o g/debian-a m/ ARM po o Debian GNU/Linux. Debian ully suppo s a po o li le-endian ARM 1999–2010 Debian po o In el IA-64 (Debian-ia64) h p://lis s.debian.o g/debian-ia64/ Discussions on he in el IA64 (aka I anium, Me ced) po o Debian GNU/Linux 2001–2010 Debian po o Alpha (Debian-alpha) h p://lis s.debian.o g/debian-alpha/ The pu pose o his p ojec is o assis de elope s and o he s in e es ed wi h he ongoing p ojec o po he Debian dis ibu ion o Linux o he Alpha amily o p ocesso s 1998–2010 Debian po o AMD64 (Debian-amd) h p://lis s.debian.o g/debian-amd64/ Po ing Debian o AMD x86-64 a chi ec u e 2004–2010 Debian po o BSD (Debian- bsd) h p://lis s.debian.o g/debian-bsd/ This is a po o he Debian ope a ing sys em, comple e wi h ap , dpkg, and GNU use land, o he Ne BSD ke nel 2001–2010 Debian po o HPPA (Debian-hppa) h p://lis s.debian.o g/debian-hppa/ This is a po o Hewle -Packa d’s PA-RISC a chi ec u e 2001–2010 Debian po o Hu d (Debian-hu d) h p://lis s.debian.o g/debian-hu d/ The GNU Hu d is a o ally new ope a ing sys em being pu oge he by he GNU g oup 1999–2010 Debian po o MIPS (Debian-mips) h p://lis s.debian.o g/debian-mips/ MIPS po o Debian GNU/Linux, able o un a bo h endiannesses 1999–2010 Debian po o Powe PC (Debian-ppc) h p://lis s.debian.o g/debian-powe pc/ Powe PC po o Debian GNU/Linux. The Powe PC a chi ec u e allows bo h 64-bi and 32-bi implemen a ions 1999–2010 Debian po o SPARC (Debian-s390) h p://lis s.debian.o g/debian-s390/ Discussions on he IBM S/390 po o Debian GNU/Linux 2001–2010 Debian po o SPARC (Debian-spa c) h p://lis s.debian.o g/debian-spa c/ This po uns on he Sun SPARCs a ion se ies o wo ks a ions, as well as some o hei successo s in he sun4 a chi ec u es 1998–2010 M.R. Ma ínez-To es / Expe Sys ems wi h Applica ions 39 (2012) 13182–13192 13187 The e olu ion o he gene ic clus e ing algo i hm is de ailed in Fig. 7. The ini ial popula ion (gene a ion 0) has a low fi ness alue, which indica es ha he indi iduals o he popula ion a e a om he op imum. As he numbe o gene a ions inc ease, he fi ness o indi iduals wi hin he popula ion also inc eases, as he gene ic algo i hm is biased owa ds he su i al o gene ic ma e ial con- ained wi hin he indi iduals wi h high fi ness unc ion alues. The op imum subse o indica o s p o ided by GA is lis ed in Ta- ble 3. In pa icula , he indica o s desc ip ion and he ne wo k o e which hey ha e been calcula ed a e de ailed. The esul s om ac o analysis using he se o a iables se- lec ed by he gene ic algo i hm a e de ailed in Table 4. Usually, a numbe o ac o s equal o he numbe o eigen alues highe han 1 is selec ed (Renche , 2002). Consequen ly, up o ou la en ac- o s can be dis inguished as esul o ac o analysis. The indica o s associa ed o each ac o a e ob ained om he ac o loadings using a Va imax o a ion. All he indica o s associ- a ed in his way wi h he same ac o a e hypo hesized o sha e a common meaning ha he analys should disco e . Table 5 shows which indica o s a e associa ed o each ac o and hei co e- sponding ac o loadings. On he o he hand, ac o sco es a e used o ca ego ize he o i- ginal sample o OSS communi ies, which can be app oxima ed o one o he iden ified la en ac o s. Consequen ly, he o iginal sam- ple o OSS communi ies can be ca ego ized in ou g oups. An anal- ysis o a iance (ANOVA) has been applied o he ca ego iza ion o Table 2 GA esul s o di e en alues o coe ficien s c1, c2 and c3. Pa ame e s (c1/c2/c3) Explained a iance Indica o s Fac o numbe In e p e abili y 1.00/0.00/0.00 77.73 20 7 0.00 0.80/0.10/0.10 79.80 49 12 0.00 0.60/0.20/0.20 78.03 46 10 0.30 0.40/0.30/0.30 73.87 53 10 0.18 0.20/0.40/0.40 75.70 49 10 0.30 0.00/0.50/0.50 72.40 48 9 0.44 0.00/0.00/1.00 59.65 14 2 1.00 0.10/0.10/0.80 70.93 23 4 1.00 0.20/0.20/0.60 71.60 36 5 0.60 0.30/0.30/0.40 74.94 49 10 0.30 0.40/0.40/0.20 77.28 51 11 0.27 0.50/0.50/0.00 75.16 52 11 0.08 0.00/1.00/0.00 72.53 55 11 0.09 0.10/0.80/0.10 72.52 54 11 0.18 0.20/0.60/0.20 75.37 54 12 0.17 0.30/0.40/0.30 76.79 53 12 0.16 0.40/0.20/0.40 75.31 43 8 0.50 0.50/0.00/0.50 73.24 22 5 0.80 Fig. 7. Fi ness dis ibu ion o e 30 gene a ions o he gene ic algo i hm. Table 3 Selec ed se o indica o s. Desc ip ion Ne wo k/subne wo k VAR02 Numbe o in e ac ions Comple e ne wo k VAR03 Numbe o epea ed in e ac ions Comple e ne wo k VAR04 Densi y Comple e ne wo k VAR06 The Zag eb g oup index Comple e ne wo k VAR09 F ee ide s Comple e ne wo k VAR10 Ac i e membe s Comple e ne wo k VAR11 Membe s esponsible o mo e han 50% o con ibu ions Comple e ne wo k VAR17 No malized size o ou pu -domain (s anda d de ia ion) Comple e ne wo k VAR18 P oximi y p es ige (a e age alue) Comple e ne wo k VAR26 Ne wo k be weenness Cen aliza ion Comple e ne wo k VAR29 Numbe o e ices wi h be weenness cen ali y >0 Comple e ne wo k VAR30 Egocen ic densi y (a e age alue) Comple e ne wo k VAR31 Egocen ic densi y (s anda d de ia ion) Comple e ne wo k VAR33 Numbe o de eloped b oke age oles among ac i e membe s Comple e ne wo k VAR34 Numbe o e ices de eloping a b oke age ole among ac i e membe s and ee ide s Comple e ne wo k VAR35 Numbe o de eloped b oke age oles among ac i e membe s and ee ide s Comple e ne wo k VAR41 Densi y Ac i e membe s ne wo k VAR42 A e age deg ee Ac i e membe s ne wo k VAR45 A e age ou -deg ee Ac i e membe s ne wo k VAR48 No malized size o ou pu -domain (a e age alue) Ac i e membe s ne wo k VAR50 P oximi y p es ige (a e age alue) Ac i e membe s ne wo k VAR53 Closeness cen ali y (a e age alue) Ac i e membe s ne wo k VAR59 Egocen ic densi y (a e age alue) Ac i e membe s ne wo k Table 4 Explained a iance o esul ing ac o analysis. Fac o Eigen alues Value Va iance (%) Cumula i e (%) 1 11.881 47.526 47.526 2 4.388 17.553 65.078 3 2.309 9.234 74.313 4 1.455 5.818 80.131 5 0.914 3.658 83.789 6 0.799 3.195 86.984 7 0.652 2.606 89.590 . . . . . . . . . . . . 23 0.000 0.001 100.000 13188 M.R. Ma ínez-To es / Expe Sys ems wi h Applica ions 39 (2012) 13182–13192 he o iginal sample in he ou g oups ob ained o m ac o analy- sis. The aim o his analysis consis s o checking he null hypo hesis o equal popula ion means. Table 6 de ails he Fs a is ic, he a io o wo di e en es ima o s o popula ion a iance, which appea s oge he wi h i s co esponding c i ical le el o obse ed signifi- cance. The esul s is ha he null hypo heses ha e been ejec ed in all he cases wi h a significance alue below 0.05. Tha means he ob ained ca ego iza ion om ac o analysis is well defined. Table 7 de ails he mean alue o he conside ed 23 indica o s pe each o he dis inguished g oups. Using his in o ma ion as well as he ac o loadings o Table 5, he ollowing websi es s uc- u e pa e ns can be dis inguished: Fac o 1: This ac o conside s high sized communi ies cha ac e - ized by a high numbe o in e ac ions and a clea hie a - chy among i s membe s. The co e g oup is loca ed on op o his hie a chy, and hey a e esponsible o de el- oping a b oke age ole among he es o communi y membe s like ac i e membe s and ee ide s. Fac o 1 includes hose communi ies wi h he highes numbe o membe s belonging o he co e g oup. Table 5 Iden ified ac o s. Desc ip ion Loading F1 VAR02 Numbe o in e ac ions 0.921 VAR03 Numbe o epea ed in e ac ions 0.900 VAR06 The Zag eb g oup index 0.836 VAR09 F ee ide s 0.800 VAR10 Ac i e membe s 0.931 VAR11 Membe s esponsible o mo e han 50% o con ibu ions 0.703 VAR29 Numbe o e ices wi h be weenness cen ali y >0 0.945 VAR33 Numbe o de eloped b oke age oles among ac i e membe s 0.929 VAR34 Numbe o e ices de eloping a b oke age ole among ac i e membe s and ee ide s 0.925 VAR35 Numbe o de eloped b oke age oles among ac i e membe s and ee ide s 0.910 F2 VAR17 No malized size o ou pu -domain 0.854 VAR18 P oximi y p es ige (a e age alue) 0.847 VAR26 Ne wo k Be weenness Cen aliza ion 0.764 VAR30 Egocen ic densi y (a e age alue) 0.881 VAR31 Egocen ic densi y (s anda d de ia ion) 0.719 F3 VAR48 No malized size o ou pu -domain (a e age alue) 0.717 VAR50 P oximi y p es ige (a e age alue) 0.901 VAR53 Closeness cen ali y (a e age alue) 0.899 VAR59 Egocen ic densi y (a e age alue) 0.740 F4 VAR04 Densi y (comple e ne wo k) 0.705 VAR41 Densi y (ac i e membe s ne w.) 0.897 VAR42 A e age deg ee 0.799 VAR45 A e age ou -deg ee 0.703 Table 6 S a is ical significance o ANOVA. FSig FSig VAR02 41.837 0.000 VAR31 16.644 0.000 VAR03 36.386 0.002 VAR33 41.910 0.000 VAR04 7237 0.003 VAR34 86.377 0.000 VAR06 24.322 0.000 VAR35 46.100 0.000 VAR09 50.931 0.000 VAR41 8018 0.000 VAR10 72.496 0.000 VAR42 10.950 0.000 VAR11 23.912 0.000 VAR45 6489 0.000 VAR17 53.598 0.000 VAR48 26.019 0.000 VAR18 40.664 0.000 VAR50 16.445 0.306 VAR26 31.039 0.000 VAR53 14.434 0.000 VAR29 73.973 0.000 VAR59 7488 0.000 VAR30 37.410 0.000 0.000 Table 7 Mean alues o selec ed indica o s. F1F2F3F4 VAR02 11096.3846 2264.8140 1935.4688 1092.2500 VAR03 8102.5385 1553.1860 1464.1250 900.3333 VAR04 0.0201 0.0558 0.0268 0.0663 VAR06 1.9473E7 1.9473E7 1.9473E7 1.9473E7 VAR09 353.6154 353.6154 353.6154 353.6154 VAR10 377.9231 377.9231 377.9231 377.9231 VAR11 8.1538 8.1538 8.1538 8.1538 VAR17 0.2353 0.2353 0.2353 0.2353 VAR18 0.0894 0.0894 0.0894 0.0894 VAR26 0.1048 0.1048 0.1048 0.1048 VAR29 198.3462 198.3462 198.3462 198.3462 VAR30 0.2611 0.2611 0.2611 0.2611 VAR31 0.3163 0.3163 0.3163 0.3163 VAR33 60910.6538 60910.6538 60910.6538 60910.6538 VAR34 55.8846 55.8846 55.8846 55.8846 VAR35 4590.7692 4590.7692 4590.7692 4590.7692 VAR41 0.0742 0.0742 0.0742 0.0742 VAR42 383725.4850 383725.4850 383725.4850 383725.4850 VAR45 152903.9688 152903.9688 152903.9688 152903.9688 VAR48 0.7834 0.7834 0.7834 0.7834 VAR50 0.2969 0.2969 0.2969 0.2969 VAR53 0.2972 0.2972 0.2972 0.2972 VAR59 0.4730 0.4730 0.4730 0.4730 Fig. 8. In e p e a ion o iden ified ac o s. M.R. Ma ínez-To es / Expe Sys ems wi h Applica ions 39 (2012) 13182–13192 13189 Fac o 2: Fac o 2 e e s o hose communi ies wi h a high local connec i i y. Communi ies ollowing his pa e n exhi- bi he highes a e age alue o egocen ic densi y and p oximi y p es ige, which means hei nodes a e highly connec ed wi h hei neighbou s. Al hough hese com- muni ies a e no so high as hose o Fac o 1, hey also exhibi an impo an size wi h a high numbe o in e ac- ions. Howe e , he le el o hie a chy is conside able lowe . The ole o he co e g oup is shaded by he high ac i i y o he es o he communi y. In ac , F2 commu- ni ies a e he ones wi h he lowes numbe o ee ide s. Fac o 3: Fac o 3 co esponds o small and cen alized ne wo ks, whe e ac i e membe s exhibi a high in ol emen and he co e g oup also pe o ms an impo an b oke age ole. This ac o includes communi ies wi h a s ong hie a chy among hei membe s bu wi h a fla e s uc- u e compa ed o F1 communi ies. Fac o 4: Fac o 4 conside s he smalles communi ies bu wi h a high densi y, which means ha ac i e membe s a e highly in e connec ed. Despi e o being smalle han F3 communi ies, hey exhibi a highe a e age deg ee alue. As a di e ence, he ac i i y o he co e g oup is shad- owed by he ac i e membe s o he communi y, so he hie a chy is much weake han in F3 communi ies. Ob ained ac o s can be in e p e ed in e ms o size and hie a - chy o communi ies, as ep esen ed in Fig. 8. This figu e g aphically isualizes he ou iden ified pa e ns o beha iou o OSS commu- ni ies. Size ep esen s how many use s he OSS p ojec is able o a - ac . The e o e, i can be in e p e ed as a measu emen o how success ul he unde lying so wa e is. Hie a chy e e s o he in e - nal o ganiza ion o he communi y. A high hie a chy means ha he co e g oup exe s an meaning- ul influence o e he es o he communi y while a low hie a chy means he e is no a dominan g oup. Fig. 9 de ails he posi ion o he conside ed Linux Debian communi ies in e ms o size and hie a chy. The gene al end is o be loca ed on he igh pa o his figu e as communi ies y o a ac as many membe s as pos- sible. As a di e ence, hey ollow di e en s a egies ega ding hei in e nal hie a chy le el. In gene al, hey end o main ain a ce ain hie a chy and only one communi y has a clea low hie a - chy le el. One o he main implica ions o his esul s is ha size and hie - a chy a e independen dimensions, so i is no incompa ible a high size wi h a s ong hie a chy. In ac , he g ow h in size impels he c ea ion o hie a chical laye s. In gene al, p ojec s gain s abili y as mo e o less o mal hie a chies eme ge. Hie a chy mainly depends on he ac i i y o he co e g oup eam. I is hei esponsibili y o canalize he discussion, o p o ide solu ions o al e na i es o he pos ed p oblems and o acili a e he inco po a ion o qualified ac- i e membe s as pa o his co e g oup. Hie a chy also causes a ise in he en y ba ie s o he co e g oup. Ou side s only can ac- qui e au ho i y inside he p ojec h ough he legi ima e pe iphe al pa icipa ion p ocedu e. The e o e, hie a chy gua an ees ha he p ojec is unde he con ol o he co e g oup o de elope s. 6. Conclusions This pape desc ibes a p ocedu e o he ex ac ion o he pa - e ns o beha iou o open sou ce communi ies using a gene ic sea ch o e a la ge se o Social Ne wo k Analysis indica o s. As a di e ence o p e ious s udies, only ocused on small se o SNA ea- u es, he p oposed e olu iona y compu a ion echnique combined wi h ac o analysis allows o conside all he possible me ics able o cha ac e ize in e ac ions among communi y membe s. Ob ained esul s show ou pa e ns o beha iou ha ha e been ex ac ed as la en ac o s om he whole da a se . These pa e ns can be in u n classified in e ms o size and hie a chy o communi ies. Analyzed communi ies can be app oached o a poin in a bidimen- sional space desc ibed by hese wo dimensions. In gene al, OSS communi ies end o gain as many membe s as possible, and hei in e nal o ganiza ion acili a es a ce ain hie a chy o eme ge. Hie a chy can be unde s ood as a s abilizing ac o o he commu- ni y ha assigns he au ho i y o a educed co e g oup membe . Access o he inne ci cle o he communi y can only be achie ed h ough a p ocess o pa icipa ion and in e ac ion wi h he es o he communi y. Size Hie a chy La ge Small High Low Debian-68k Debian-ARM Debian-ia64 Debian-alpha Debian-amd64 Debian-BSD Debian-hppa Debian-hu d Debian-mips Debian-ppc Debian-s390 Debian-spa c Fig. 9. Pa e ns o beha iou o Debian Linux po s communi ies. 13190 M.R. Ma ínez-To es / Expe Sys ems wi h Applica ions 39 (2012) 13182–13192