Analyzing Patterns of User Content Generation in Online Social Networks

Transcription

1 Aalyzig Patters of User Cotet Geeratio i Olie Soial Networks Lei Guo, Ehua Ta, Sogqig Che, Xiaodog Zhag, ad Yihog (Eri) Zhao Yahoo! I. 7 First Aveue Suyvale, CA 989, USA {lguo,yzhao}@yahoo-i.om Dept. of Comp. Si. & Egr. Ohio State Uiversity Columbus, OH, USA {eta,zhag}@se.ohio-state.edu Dept. of Computer Siee George Maso Uiversity Fairfax, VA, USA sqhe@s.gmu.edu ABSTRACT Various olie soial etworks (OSNs) have bee developed rapidly o the Iteret. Researhers have aalyzed differet properties of suh OSNs, maily fousig o the formatio ad evolutio of the etworks as well as the iformatio propagatio over the etworks. I kowledge-sharig OSNs, suh as blogs ad questio aswerig systems, issues o how users partiipate i the etwork ad how users geerate/otribute kowledge are vital to the sustaied ad healthy growth of the etworks. However, related disussios have ot bee reported i the researh literature. I this work, we empirially study workloads from three popular kowledge-sharig OSNs, iludig a blog system, a soial bookmark sharig etwork, ad a questio aswerig soial etwork to examie these properties. Our aalysis osistetly shows that () users postig behavior i these etworks exhibits strog daily ad weekly patters, but the user ative time i these OSNs does ot follow expoetial distributios; () the user postig behavior i these OSNs follows strethed expoetial distributios istead of power-law distributios, idiatig the ifluee of a small umber of ore users aot domiate the etwork; () the distributios of user otributios o high-quality ad effort-osumig otets i these OSNs have smaller streth fators for the strethed expoetial distributio. Our study provides isights ito user ativity patters ad lays out a aalytial foudatio for further uderstadig various properties of these OSNs. Categories ad Subjet Desriptors H. [Iformatio Systems]: Models ad priiples Geeral Terms Huma Fators, Measuremet Keywords User geerated otet (UGC), soial etworks, strethed expoetial distributio. INTRODUCTION Reet years have witessed the suess of a umber of olie soial etworks (OSNs), suh as Del.iio.us ( deliious.om/), Faebook ( Permissio to make digital or hard opies of all or part of this work for persoal or lassroom use is grated without fee provided that opies are ot made or distributed for profit or ommerial advatage ad that opies bear this otie ad the full itatio o the first page. To opy otherwise, to republish, to post o servers or to redistribute to lists, requires prior speifi permissio ad/or a fee. KDD 9, Jue 8 July, 9, Paris, Frae. Copyright 9 ACM /9/...$.. Flikr ( LikedI ( likedi.om/), Yahoo! Aswers ( om), ad YouTube ( These soial etworks have attrated a sigifiat umber of partiipats that otribute various otets o the Iteret, whih is ofte referred to as user geerated otet (UGC), owig to the pervasive broadbad Iteret aesses ad the everireasig badwidth available to ed users []. Users are basi elemets of these OSNs ad ommuities. I geeral, a user s ativities i OSNs ilude authorig otet, viewig, ad etworkig. Aordig to their differet purposes, existig OSNs a be lassified ito two ategories, the etworkig orieted OSNs ad the kowledge-sharig orieted OSNs. The former, suh as Faebook ad LikedI, emphasizes more o the etworkig perspetive, ad the soial relatioship is the basis of these OSNs. Hee, we all them etworkig orieted OSNs. I these OSNs, otet sharig is maily amog frieds. The latter, suh as blog etworks, questio aswerig etworks, ad viral video etworks, emphasizes more o the kowledge or otet sharig. Thus, we all them kowledge-sharig orieted OSNs. The etwork i these OSNs is ot drive by the uderlyig soial relatioships. Istead, the etwork is formed through the users ommo iterests o the shared otet. The rapid developmet of these OSNs has attrated sigifiat attetios from researh ommuity. A umber of studies [,,,, ] have bee oduted to examie various properties of differet OSNs. For example, Cheg et al. [] studied the YouTube videos ad foud that the liks to related videos geerated by uploaders hoies have lear small-world harateristis, whih idiates that the videos have strog orrelatios with eah other. I work [], based o four large olie soial etworks, the authors studied the evolutio of soial etworks ad showed that the ombiatio of the gap distributio with the ode lifetime leads to a power law out-degree distributio that aurately reflets the real etwork i all four ases. I blogspae, works [, ] have studied the lik propagatio ad iformatio epidemis. However, these existig studies maily foused o how users are oeted ad thus how the etworks are formed, as well as how a soial etwork graph evolves over time, suh as []. Users who have a large umber of oetios are the ore of soial etworks, ad play a importat role o iformatio propagatio. But i kowledge-sharig orieted OSNs, how users partiipate i the etwork ad how users geerate ad share otet play the key role i attratig viewers, sie the user partiipatio ad otributio i these OSNs drive the growth of these soial etwork ommuities ad the suess of their busiess. Therefore, uderstadig the patters of user partiipatio ad user postig behavior i these kowledgesharig orieted OSNs is very imperative to soial etwork idustry ad researhers, i order to idetify ad distiguish

2 ative users from spammig users, attrat ew users ad keep existig users, predit hot spots ad the treds of topis i user ommuities, ad perform effiiet resoure maagemet i the uderlyig supportig system. The user partiipatio i terms of ative time i peer-topeer ad soial etworks has bee assumed to follow expoetial distributios i modelig [9, ], ad it has bee also assumed that there is strog orrelatio betwee user ative time ad user otributio. It had bee reported that i Wikipedia, most of artiles are otributed by a small umber of users []. I [], Voss foud that both the umber of Wikipedia artiles a user edited ad the umber of authors for a Wikipedia artile follow power law, for otets of differet laguages. I [], Kittur et al. aalyzed the edit logs of Wikipedia from to, ad fid a shift of the user otributios from a ore group of elite users to ommo users, i terms of both umber of edits ad legth of revised otets. A similar shift of user otributio distributio for Del.iio.us soial etwork was also reported i []. However, whether the user otributio i Wikipedia/Del.iio.us follows power law or ot is ot further aalyzed. O the other had, some studies have bee oduted o the distributio of user partiipatios i etworkig orieted OSNs. For example, Seshadri et al. studied the mobile phoe all graph as a soial etwork ad aalyzed the distributio of the legth of mobile alls []. They foud it does ot follow power law or logormal. Istead, the double Pareto LogNormal fits the data very well. Gjoka et al. [7] studied the appliatios o Faebook ad foud that although the umber of appliatio istallatios ireases with time, the average user ativity dereases. These fidigs have put the ommoly aepted power law assumptio i doubt. I this work, we set to study the user otributios ad ativities i kowledge-sharig orieted OSNs empirially. For this purpose, we have aalyzed three workloads of popular OSNs, iludig blog, bookmark sharig, ad questio aswerig soial etworks for a duratio of multiple years. I these OSNs, we are partiularly iterested i how users partiipate i the etwork, geerate or post otet, as well as the quality of the otet. We have the followig fidigs i this study:. User postig behavior of origial otet i these OSNs shows strog daily ad weekly patters. However, for o-origial otet postig (i.e., otet ut-adpasted from other soures), we have ot observed temporal postig patters (or patters alog time).. We have observed two groups of users with distit postig behaviors: () steadily postig i the etwork, () iatively postig. The rest users post oasioally i the etwork. The overall user lifetime does ot follow the expoetial distributio.. The distributio of differet users postig ativities does ot follow power law distributios. Our aalysis aross three workloads from both short terms (i weeks) ad log terms (i years) osistetly shows that it follows the strethed expoetial distributio, for whih the idividual otributios of top users are distributed muh flatter tha those i power law etworks.. We have observed that the strethed expoetial distributio of user otributios i OSNs roughly follows the 8- rule, i.e. % users otribute 8% total otet i the etwork. However, the umulative otributio ratios of a small umber of top-k users i the OSNs are muh smaller i OSNs tha those i stadard power law distributios, suh as Pareto s soial wealth distributio. This implies that otets i a OSN are ot maily otributed by a small umber of ore users.. Users otribute differet types of UGC objets. Their otributios a be haraterized by the strethed expoetial model with differet parameters. For example, the distributio of user otributios o highquality otet teds to have a small streth fator, idiatig that it is more skewed towards (a few) ore users. Our fidigs provide isights ito user behaviors of OSNs, whih is timely desirable i soial etwork idustry ad researh ommuity. We hope our aalysis lays out a foudatio to guide the desig, modelig, ad simulatio of large ad omplex OSNs with various properties for may appliatios. The remaider of this paper is orgaized as follows. We preset related works i Setio. I Setio, we overview the soial etwork systems studied i this work. Our detailed workload aalysis is oduted i Setio. We further aalyze the impliatios of our fidigs i Setio ad make oludig remarks i Setio.. RELATED WORK Olie soial etworks have attrated osiderable attetio reetly. A umber of studies have bee oduted o differet forms of soial etworks. For example, as oe of the typial soial etwork domai o the Iteret, blogspae has ostatly attrated researhers attetio. Earlier work [,, ] had foused o the lik propagatio behaviors i blogsphere ad studied the iformatio epidemis. While asadig behaviors were rare i [, 8], Leskove et al. [9] aalyzed about thousads blogs ad. millio postigs, reported that the size of the asades distributio follows a perfet Zipf distributio with the slope value of. Aordigly, a flu-like epidemiologial model is proposed to haraterize the asades i blogspae. Gruhl et al. [8] studied the dyamis of iformatio propagatio at both topi ad idividual levels i blogspae. They showed that topis are omposed as a uio of log term hatter topis ad short-term spike topis. At the idividual level, they propose a model for iformatio diffusio based o the spread of ifetious diseases []. Besides blogs, various other olie soial etworks have also bee studied. For example, Xiao, Guo, ad Traey [7] studied the istat messagig (IM) etworks ad foud that the soial etwork of IM users does ot follow a power law distributio; istead, it a be haraterized by a Weibull distributio. Leskove et al. [7] studied Mirosoft Messegers ad foud the average path legth amog users is.. The empirial results of soial etwork ommuity struture ad evolutio have also bee reported. For example, Leskove [8] et al. aalyzed about 7 large etworks ad foud that ommuity struture is differet from what have bee reported, ad proposed a forest fire geerative model to haraterize suh strutures. I work [], based o four large olie soial etworks, authors studied the evolutio of soial etworks ad showed that the ombiatio of the gap distributio with the ode lifetime leads to a power law outdegree distributio that aurately reflets the true etwork i all four ases. O the other had, aalytial models have also bee studied for soial etworks for a log time. For example, work [] aimed to fid the most ifluetial odes ad build probabilisti models for viral marketig, ad work [] tried to fid the most ifluetial odes i several of the most widely studied models i soial etwork aalysis. I [], authors performed theoretial aalysis o iformatio asades based o radom graphs while i [] authors aalyzed topologial asade patters i a large produt reommedatio etwork empirially.

3 .. Weekly patter.. Weekly patter. Weekly patter. Weekly patter Mo Tue Wed Thu Fri Sat Su Mo Tue Wed Thu Fri Sat Su Mo Tue Wed Thu Fri Sat Su Mo Tue Wed Thu Fri Sat Su Daily patter Daily patter Daily patter Daily patter 9 8 (a) Blog Artile postig 9 8 (b) Blog Photo postig 9 8 () Bookmark postig Figure : Weekly ad daily patters of UGC postig i OSNs 9 8 (d) Aswer postig Amog these soial etworks, user ativities ad the UGC play a key role, partiular to kowledge-sharig orieted OSNs. Work [] proposed fast algorithms to haraterize bursty patters of user postig ativities i blogspae. Suh bursty patters are ofte regarded as the result of heavy-tailed dyamis, ad power law distributios [, ] are ofte used to haraterize suh attributes. I PP etworks, Stutzbah ad Rejaie have also studied the hurs aused by user ativities []. Sie user ativity patters i kowledge-sharig orieted OSNs have ot bee well studied despite of their sigifiae, we set to study suh patters ad its impliatios i this work. Our empirial aalysis provides several ew fidigs that are differet from the ommoly aepted oepts about user ativities ad otributios i these OSNs.. USER ACTIVITY AND UGC CONTENT CREATION OVER TIME I this study, we aalyze three OSN workloads. The Blog workload otais the DB dump of a blog system with millios of users i Asia, iludig all posts of artiles ad photos for multiple years. We will refer them as Blog Artile (or Artile) ad Blog Photo (or Photo), respetively. The Bookmark workload is from the DB dump of a well kow soial bookmark sharig etwork i U.S., iludig all bookmarks posted for a umber of years. The Aswer workload otais the DB dump of a famous questio aswerig soial etwork i U.S., iludig all questio ad aswer posts for several years. I our study, we oly osider objets posted by users. User ommets, suh as ommets of a blog artile by the blogger s frieds, are ot osidered as UGC posts. Before we preset the detailed aalysis results, we first preset a overview of user postig ativities ad the posted otet i this setio.. Daily ad weekly patters All three soial etworks i our study are expadig with time. I geeral, the umber of daily ew posts ireases with time sub-liearly, while the umulative umber of all posts ireases with time super-liearly. For Bookmark ad Aswer, the daily umber of ew posts for weekdays ad weekeds show differet patters. To uderstad these weekly patters further, we study the umber of posts i differet weekdays ad weekeds. We bi UGC posts by hours, ad out the umbers of posts i the same hours by weeks, for the three OSNs. We the ormalize the umber of posts i eah hour by the total umber of posts aross the etire trae duratio. The upper plots of Figure show the ormalized weekly posts for Blog Artile, Blog Photo, Bookmark, ad Aswer, respetively. We a see for Bookmark ad Aswer systems, the hourly umber of posts i weekdays is muh higher tha the hourly umber of posts i weekeds. For Blog systems, the hourly umber of posts is similar durig weekdays ad weekeds. This is beause bloggig is a kid of daily Web jouralig or diary writig, so the daily user ativities o blog postig do ot hage dramatially aross differet days i a week. The bottom plots of Figure further show the daily patters of UGC postig, omputed i a similar way as that of weekly patters of UGC postig. For all three OSNs, the peak time for postig is about : i loal time. However, the least ative time for blog artile/photo postig is :, whih is differet from bookmark/aswer postig (:-:), idiatig differet user ativity patters i these OSNs.. User/otet irease rate i OSNs To study the statistis of user otributios i OSNs, a ommo method is to osider the uio of all users ad all posts i the system durig a measuremet period. However, users may joi the system at differet time i this period. For large sale measuremets, the umber of ew users i this period a be o-trivial ad the joiig rate a be bursty. Figure shows the daily umber of ew users joied i Blog ad Bookmark systems for a seleted period i the workload duratio (the startig dates are hided for the purpose of busiess ofidetial protetio). I additio to the weekly ad daily flutuatig patters of ewly joied users, the user joiig evets are bursty i daily, weekly, ad eve a larger time sale. For example, as show i Figure (a), aroud time t, i the trae olletio duratio, the umber of ew users is sigifiatly higher tha that before ad after t. For Bookmark, as show i Figure (b), there are a umber of spikes, idiatig bursts of user joiig evets spreadig over a umber of weeks. Figure (a) shows the daily irease rate of users ad artile posts o the left y-axis, ad the overall otributio per user o the right y-axis for the Blog system with time, for the same time period i Figure (a). The daily user (post) irease rate is defied as the ratio of the umber of ewly joied users (ewly posted artiles) i a day over the umulative umber of users (artiles) by the last day. The overall otributio per user by a day is defied as the ratio of the umulative umber of posts i the system by that day over the umulative umber of users that have joied the system by that day. I geeral both the post irease rate ad the user irease rate derease with time gradually, meaig the total umbers of both posts ad users irease with time super-liearly but ot expoetially. Furthermore, the post irease rate is always greater tha the user irease rate exept aroud t. We a see that both the daily user irease rate ad the post irease rate aroud t are greater tha those i the eighborig days otieably. However, the ratio of the post irease rate to the user irease rate i that day is smaller tha those i the eighborig days. This meas the burst of these ew users have less otributios tha the average user i the system. As a result, the overall otributio per user does ot irease o that day ad the irease beomes liear after that. I otrast, aother user irease burst aroud t does ot affet the overall otributio per user muh.

4 . Averge # of posts per user so far. Averge # of posts per user so far # of ew users 8 t t Time (day) (a) Blog # of ew users 8 Time (day) (b) Bookmark Figure : Daily umber of ew users over time i OSNs Daily user/post irease rate... Daily user irease rate Daily post irease rate Time (day) (a) Blog (daily) Averge # of posts per user so far Weekly user/post irease rate.8... Weekly user irease rate Weekly post irease rate Time (day) (b) Bookmark (weekly) Figure : User/post irease rate ad overall otributio per user i OSNs 8 Averge # of posts per user so far CDF.8... blog bookmark aswer 8 Author age of posts (day). blog bookmark aswer 8 User ative duratio (day) (a) CDF of author age of posts (b) CDF of user ative duratio Figure : User ativity over time Figure (b) shows the weekly irease rate of users ad posts o the left y-axis, ad the overall otributio per user o the right y-axis for the Bookmark system with time, for the same time period i Figure (b). Similar to the user/post irease rate i Blog, the weekly user/post irease rate is defied as the ratio of the umber of ewly joied users i a week over the umulative umber of users by the last week. Similar to those i the Blog system, both the post irease rate ad the user irease rate derease with time gradually. However, from the figure, we a see that i the week sale, the user irease rate a be greater tha the post irease rate, whih is very rare i the Blog system. Compared with Figure (b), we a see the spikes where the user irease rate is greater tha the orrespodig post irease rate are aused by the bursts of user joiig evets, ad these joied users have less otributios tha ommo users. Sie eah of suh bursts a last for weeks, the user irease rate atually flutuates quite big i this time sale, though the geeral tred is still desedig. As a result, as show i Figure (b), the overall otributio per user flutuates i a time sale larger tha weeks, ad fially ireases liearly at a low rate.. User ativity over time ad user lifetime Previous studies assume user s lifetime follows expoetial distributios ad user ativity is uiform over its lifetime or dereases with time expoetially [9, ]. Uderstadig user ativity over time is importat to model the formulatio ad evolutio proess of soial relatioships i a soial etwork, as well as the aess ad reatio traffi of UGC otet i a etwork. I order to study user postig ativity over time, we ompute the author age of eah UGC objet i the workloads. The author age of a UGC objet is defied as the iterval from the time whe a user jois the etwork to the time whe the objet is posted. A uiform distributio of author age of UGC objet meas user ativity is uiform over time, while a expoetial distributio of author age of UGC posts meas user ativity dereases with time expoetially. Sie all three OSNs are expadig over time, the daily umber of UGC postig ireases with time. To avoid biased estimatio, we selet users that joied the system i the same CDF.8.. week, ad extrat the author age of eah post by these users. Figure (a) shows the CDF distributio of the author age of posts i Blog, Bookmark, ad Aswer OSNs. For the Bookmark OSN, we a see this distributio is almost uiform, meaig most users bookmarkig ativities do ot hage over time due to regular Web browsig. For Blog, posts are a little more oetrated o small author ages tha Bookmark, but the mai body is lose to uiform too sie may users ted to post blogs regularly. For Aswer, the umber of posts with large author ages is eve smaller, ad beomes uiform whe the author age of postig is greater tha days. Beause aswerig questios is a kid of altruism behavior, a user may beome lazy after providig suh servies for a ertai time duratio i the Aswer system. Eve so, the user ativities i all these etworks are still ot expoetially dereasig with time. Figure (b) shows the CDF of user s ative duratio, the duratio from the user joiig time to the last user postig time i our traes. The figure idiates that i all three OSNs, there are a umber of users who either have short ative duratios or have log ative duratios (espeially for Blog ad Bookmark). If we assume a user will ot retur to the OSN after a log iative time, a short ative duratio represets a short user lifetime. This meas there exist two kids of users i OSNs: users with short ative duratios just try the soial etwork system for a short duratio ad the ever or rarely post later; users with log ative duratios keep postig with time, leadig to the uiform body i the CDF of author age of posts. Our aalysis of user ativity over time ad user lifetime idiates user s lifetime does ot follow expoetial distributio, while user ativity is quite uiform over its lifetime. However, the ativity frequey of users may vary sigifiatly, whih a be haraterized through the distributio of user otributios i OSNs. We preset this study i the ext setio.. THE DISTRIBUTION FUNCTION OF USER CONTRIBUTIONS The workload overview study i the last setio provides us some isights o the user ativities alog time. I this setio, we further examie user otributios beause i kowledgesharig orieted soial etworks, the otet otributed by users is the key to attrat users ad drive the growth of the etwork.. Origial ad o-origial UGC otet Before we start, we shall larify that we are oered about the origial otet reated by users. I geeral, there are three types of UGC objets i OSNs. The first is the origial UGC objets, reated by the user who posts them. The seod is o-origial otet obtaied through uttig-ad-pastig, ad the third is advertisemet ad spam. Sie maily viewers are attrated by the origial UGC, we thus fous o the

5 Figure : The average postig itervals of bloggers.. Weekly patter Mo Tue Wed Thu Fri Sat Su Daily patter 9 8 Figure : Weekly/daily patters of ut-ad-paste bloggers Number of posts.... x Life Photography Travel Workig Study Creatio Musi Movie Relatioship Family Pop Culture Leisure Habits Tehology Produts Computer/Iteret Game Food Soial Evets Rereatio Art Desig Sport Religio/Philosophy Eviromet/Health Busiess Orgaizatio Alterative Figure 7: Forwarded posts i differet blog ategories first type for the study. Therefore, first we eed to differetiate ad filter out the seod ad the third types of otet from the workloads. Amog the three OSNs we study, Blog maily otais origial UGC ad o-origial otet forwarded from other plaes. The advertisemet ad spam otets have bee idetified ad removed usig mahie learig based approahes whe buildig searh idex for the system. The advertisemet ad spam posts i Bookmark ad Aswer system are filtered out with a similar method as Blog system durig searh idex buildig period. Furthermore, i Aswer, sie a user who asks a questio a sore the aswers posted, a perso who posts urelated aswers will ot ear redits. Thus, we maily eed to filter out o-origial otet i Blog Artile. Figure shows the average postig iterval ad the total umber of posts for eah blogger. We a see there are a small umber of bloggers who post a large umber of artiles with small itervals. These bloggers just ut-ad-paste etertaimet ews ad politial ews from the Web to their ow blogspaes. We all these blog posts as forwarded posts. Figure shows the weekly ad daily postig patters of these ut-ad-paste bloggers. I otrast to Figure, the figure shows o oetrated peak time for forwarded blog postig, idiatig that these users are usig ut-ad-paste at ay time i a day. Figure 7 further shows the umber of suh posts i differet artile ategories (the blog ategory is seleted by the blogger whe post). The rereatio ategory aouts for most forwarded posts, ad the soial evets ategory raks the seod. Istead of idetifyig ad removig all forwarded posts, we remove all artiles of bloggers whose average postig iterval is less tha / day ad have posted at least posts altogether, orrespodig to a total of users (.%) ad.9% artiles. Sie our purpose is to study the distributio of the umber of origial posts by eah blogger, whih is heavy-tailed, igorig forwarded posts of users who post a small umber of artiles (i total) shall ot affet the distributio muh.. Strethed expoetial distributio of user otributio Sie we are iterested i the otributio of eah user o the origial otet i a OSN ad the variae amog differet user s otributios, it is atural to rak all users aordig to their otributios ad the idetify those with high otributios. If we sort eah user by the umber of posts i desedig order, the futio of a user s post umber to his/her rak order is alled the rak order distributio futio i the soial etwork. If we ormalize the rak order by dividig the total umber of users i the soial etwork, the the iverse futio of a ormalized rak order distributio futio is idetial to a omplemetary umulative probability distributio futio (CCDF). With the rak distributio, we a fous o those ative users who otribute a large amout of high quality UGC otet. The well kow Zipf distributio is a rak order distributio, also kow as power law. The power law distributio a be expressed as y i i α ( i ), where y i is the value, i is the rak, ad α is a ostat. The power law distributio has bee widely used i haraterizig the Iteret, WWW, ad soial etworks. To aalyze the user otributio distributio i depth, Figure 8 shows the distributio of user posts for six types of UGC objets i these three OSNs. I eah figure, the x oordiate represets the referee rak of eah user, plotted i log sale, while the y oordiate represets the umber of UGC objets posted by this user, plotted i both log sale (marked o the right of y-axis) ad a powered sale (by a ostat, as marked o the left of y-axis). We all the ombiatio of log sale i x ad powered sale i y as the strethed expoetial (SE) sale. Note for Blog Artile show i Figure 8(a), the ut-ad-paste bloggers have bee removed. Bookmark Imports i Figure 8(d) represets the bookmarks a user imports from her existig bookmark whe joiig the Bookmark etwork. Sie i the Aswer etwork, a asker a selet a aswer for her questio as the best aswer, we plot the best aswers that eah user otributes i Figure 8(f), separated from the overall aswers i Figure 8(e). These figures show that i log-log sale, the post rak distributios of users i OSNs have a flat head ad a steep tail, whih aot be fitted with a straight lie, idiatig they are ot power law. However, by seletig a proper ostat, all these workloads a be well fitted with a straight lie i SE sale. The first several poits i Figure 8() ad 8(d) are muh higher tha the lie predits, whih is alled Kig effet []. Suh a rak distributio is alled a strethed expoetial distributio. The strethed expoetial distributio has bee used to haraterize the aess patters of Iteret media traffi []. Its orrespodig CCDF futio is the Weibull futio P(X x) = e ( x x ), () where ad x are ostats. If we rak the elemets i a data set i desedig order of the data value x i ( i ), we have P(X x i) = i/. Substitute x i for y i, the rak distributio futio a be expressed as follows y i = alog i + b ( i ), () where a = x ad b = y. Thus, the data distributio is a straight lie i log-y plot. If we assume y =, we have b = + alog. ()

6 989 =., a=.7, b =.9 Rak (log sale) (a) Blog Artile posts 78 =., a=.8, b =. 7 R =.98 data i log y sale Rak (log sale) (b) Blog Photo posts Rak (log sale) () Bookmark posts 7 =., a=., b =.98 R = =., a=.98, b =.88 R = data i log y sale data i log log sale Number of posts (y sale) Number of posts (log sale) # of Referees (y sale) 7 8 data i log log sale =.9, a=., b = 7. R =.9997 Rak (log sale) (d) Bookmark imports data i log y sale Number of posts (log sale) data i log log sale Number of posts (y sale) data i log y sale 9 9 R =.999 # of Referees (log sale) data i log log sale 97 data i log y sale # of Referees (y sale) # of Referees (y sale) 7 # of Referees (log sale) # of Referees (y sale) data i log log sale 7 =.8, a=.9, b = 7.7 R = # of Referees (log sale) data i log log sale # of Referees (log sale) 8 Rak (log sale) data i log y sale (e) Aswer posts (overall) Rak (log sale) (f) Aswer posts (best) Figure 8: Strethed expoetial distributio of user posts i OSNs To get the parameters of a strethed expoetial distributio, we use the maximum likelihood estimatio method (MLE): assumig a data set {x, x,..., x } follows some probability distributio with ukow parameters, the most probable parameters are parameters that make the produt of the probability desity futios of eah elemet i the data set maximum. Deote the parameter vetor as θ, the θ = arg maxθ Y pθ (xi ). () i= The probability desity futio of a Weibull distributio (strethed expoetial) is p(x) = x ( xx ). e x Thus, we have P 8 X i= (yi log yi y log y ) P = log yi, < i= i= (yi y ) X (yi y ). : a = i= () () We first get parameter with the iteratio method, the we get parameter a. With Equatio, parameter b a be estimated as X (y + a log i). (7) b= i= i However, i our study, the data to be fit (the umber of UGC otet a user reates) are positive itegers, while the radom variables i a Weibull distributio are real umbers. Sie there is o data elemet smaller tha oe, the parameters give by the MLE method above may result i o-trivial errors i the strethed expoetial plot. I order to miimize the model fittig errors aused by the disreteess of data values, espeially data elemets equal to oe, a iterative fittig tehique is utilized, desribed i the followig. We use the oeffiiet of determiatio of the data fit, also kow as R, as a idiator of fittig errors 8 X SSE = w(i)(yi ( a log i + b) ), i= < X (8) SST = w(i)(yi yi ), i= SSE : R =, SST where SSE is the sum of weighted squares due to errors, SST is the total sum of weighted squares about the mea, ad w(i) is the weight of data poit yi. Sie the strethed expoetial fit is oduted i log sale o the x-axis, we selet w(i) = (log i) = /i. The loser R to, the better the model fits the data. We iteratively truate the raked sequee {yi } ( i ) by removig the last k elemets that equals to oe i the sequee, the estimate parameters for the truated sequee usig the MLE method, util the R value with the estimated parameters is losest to or larger tha a threshold. To avoid bias o the fittig error estimatio, all elemets i the sequee (iludig the k elemets ut off) are osidered whe omputig R. Our matlab pakage for strethed expoetial fit a be dowloaded from Model validatio I order to evaluate the goodess-of-fit of the strethed expoetial distributio o the data, we odut Chi-square test as follows. We divide the data value rage ito k bis (k ) as evely as possible, with eah bi has at least data poits (tail bis are merged whe eessary). The Chi-square sum is omputed as follows χ = k X (Oi Ei ), Ei i= (9)

7 Table : Chi-square test results (α =.) Data set k χ χ (α,k ) Result blog artile..7 blog photo.7.7 bookmark post.8.9 bookmark import all aswer post.97.7 best aswer post 7..9 Number of posts (y sale) =., a=.7, b =.7 R =.9898 data i log log sale data i log y sale Rak (log sale) Figure 9: User posts i Blog (users that joi system i the same week) where O i is the observed frequey of i-th bi, E i is the expeted frequey of i-th bi, ad k is the umber of bis. Assume the sigifiae level is α (i our test α =.), the assumed distributio is rejeted whe χ χ (α,k ) () where χ (α,k ) is the Chi-square futio, k is umber of bis ad is the umber of distributio parameters plus. The results of our test are preseted i Table. All data fittigs pass the Chi-square test (same as R omputatio, all elemets i the data set are osidered i Chi-square test). We have also tried power law ad logormal fits o these data sets, however, oe of them a pass the Chi-square test. Figure 8 iludes all users i the etire workload. For user otributio i a short duratio of eah workload, the strethed expoetial distributio still holds, with the same strethed fator. However, as we have preseted before, the umber of users ireases with time super-liearly. Durig the etire workload, some users may beome iative with time. I order to elimiate the effet aused by users of differet ages, we selet users who joi the system i the same week ad study their otributios durig a etire year. Our results show that the user otributios are still well fit with SE distributios with early the same streth fator (examied by Chi-square test). Figure 9 shows the fittig results for Blog Artile. Due to page limit, we omit other figures.. IMPLICATIONS OF CONTRIBUTION DISTRIBUTIONS OF OSN USERS The strethed expoetial distributio of user otributios has a umber of impliatios that are differet from those based o a power law model. We aalyze some of these impliatios i this setio.. The 8- rule ad ore users i OSNs Figure shows the umulative otributio ratio of top users (over all otributio by all users) i OSNs. As show i the figure, the umulative otributio of top users i the tree OSNs roughly follows the so alled 8- rule: i Blog, the top % users aout for 8% posts; i Bookmark, the Number of posts (log sale) Table : Top-k ore users i OSNs Data set a k/ umsum Blog Artile.9.8 7, Blog Photo.79. 8, Bookmark..,77,.8.7 Aswer.98.,,9.7.7 top.% users aout for 8.% posts; i Aswer, the top % users aout for 87% posts. However, the 8- rule of the strethed expoetial distributio is differet from that of the power law distributio. Cosider the umulative otributio ratio of top-k users i a power law rak distributio y i i α ad a strethed expoetial rak distributio y i = a log i + b ( i i both distributios), deoted as T se ad T pow, respetively. Figure shows the ompariso of T se ad T pow with log sale i x axis. The parameters of the SE plot are based o the blog artile data, while the skewess fator of the power law plot, α, is set to.9. We a see although the two urves iterset at the 8- poit, for a small k, the umulative otributio ratio of top k users i a strethed expoetial etwork is muh smaller tha that i a power law etwork. Whe, for a limited value of k, we a prove T se = lim T pow k P k i= ( + alog ) =. () i α a Γ( + )( α)α The aalysis above idiates that i otrast to a power law distributio, a strethed expoetial distributio is less skewed, meaig a small umber of top users aot domiate the etwork as those i power law etworks. This a be refleted from the log-log plot of the user otributio rak distributio. As show i the log-log plot of Figure 8, the user otributio distributio urve has two modes i geeral. The first mode is quite flat, orrespodig to a small umber of top users, where the hage rate of user otributio dereases with the hage rate of user rak k slowly. The seod mode is muh steeper, orrespodig to the majority of users, where the hage rate of otributio dereases with the hage rate of rak k sigifiatly. This observatio motivates us to idetify those ore users ad the orrespodig otributios i a soial etwork with the top-k aalysis. For this purpose, we selet a rak k so that for users with a rak i k, the derease rate of user otributio is smaller tha the irease rate of user rak. Thus for i = k, we have dy(i) y(i) + di dlog y(i) =, i.e., =. () i dlog i Let X = log i ad Y = log y. Figure shows a strethed expoetial distributio urve i log-log sale. Lie AB with slope is taget to the SE urve at poit (X, Y ). So the geometri meaig of k is that k = exp(x ), ad we have X = b a. () Assumig b = + alog (Equatio ), we have k = exp( a ). () Table shows the umber of top-k ore users for differet kids of UGC objets i OSNs. Colum umsum is the umulative otributio ratio of total otet i the OSN for top-k ore users. I geeral about % to % users a be osidered as ore users i OSNs. However, the umsum of

8 Cumulative otributio of total.8... blog bookmark aswer 8 Top users (%) Cumulative otributio ratio.8... SE (blog artile) Power law (α =.9) Fratio of users Number of posts A (X, Y ) B User rak Figure : Cumulative otributio ratio of top users i OSNs these top-k ore users are quite lose for all ases, ragig from % to 7%. The same method a be applied to estimate popular objets i otet sharig OSNs where the request patters follow strethed expoetial distributios.. Differet UGC reatio patters i OSNs The 8- rule of user otributio i OSNs idiates a small fratio of users otribute most otet i the etwork. However, this metri is quite rough, ad aot reflet the iequality of users kowledge otributios i OSNs. The top-k aalysis based o strethed expoetial model provides a quatitative method to haraterize the oetratio of UGC otributios from differet users. To further uderstad the iequality of users otributios o UGC objets of differet types, we odut the strethed expoetial fit o differet duratios of the three data sets. Our results show that, although differet duratios of data set have differet umbers of users ad UGC objets, parameter is almost a ostat for the same soial etwork system ad otet type aross differet duratios, while parameter a varies for differet duratios. We have also studied differet lasses of objets i the Blog soial etwork, by osiderig blog artiles of differet sizes ad differet umbers of tags attahed by the authors. The strethed expoetial parameters of differet UGC objets are listed i Table. As show i the Table, the parameter for best aswer posts is smaller tha that of all aswer posts, ad the parameter for blog photos is smaller tha that of blog artiles. I otrast, for Bookmark, the parameters for bookmark posts (bookmarks geerated with Bookmark plugi) ad imported bookmarks (bookmarks geerated with Web browser, whih are imported to the Bookmark whe a user jois the system) are almost the same. We ojeture that parameter reflets the quality of a UGC objet or the effort of reatig a UGC objet, whih may haraterize some itrisi property of UGC objets i soial etworks: the more effort a user eeds to make to reate a UGC objet, the smaller is. I the Aswer system, the best aswer s are seleted by the user who asked the questio, thus the otet quality has bee judged by the asker herself. If we assume high quality aswers eeds more effort to reate tha low quality aswers, the the distributio of user otributio for best aswer posts, whih are effort-osumig, would have smaller tha that for ormal aswer posts. For Blog system, it is easy to uderstad that loger artiles eed more effort to ompose tha shorter artiles, ad seletig tags for a artile eeds extra effort. It is also uderstadable that omposig a short blog artile i the Web browser eeds less effort tha takig a photo, trasferrig it to a omputer, makig some edit work suh as resalig, ad the uploadig it to oe s blogspae with some text desriptios. O the other had, it is straightforward that there is o sigifiat differee be- Figure : Cotributio of top users i SE ad power law etworks Figure : Top user seletio Table : Strethed expoetial parameters for differet types of UGC otets UGC workload a Blog Artile (all posts).8.9 Blog Artile (with tags)..7 Blog Artile ( KB).9. Blog Artile ( KB)..7 Blog photo..7 Bookmark (imports).. Bookmark (all posts)..8 Aswer (all posts)..98 Aswer (best aswers).9. twee the effort of bookmarkig a Web page usig a Web browser ad that usig a Bookmark plug-i. However, it is hard to ompare Blog/Aswer posts ad Bookmark posts diretly sie the postig mehaisms ad user otributios of these two kids of UGC objets are sigifiatly differet. For Wikipedia, the effort of omposig a Wikipedia artile a be muh greater tha that of omposig a good aswer for a user asked questio. If we assume that the user otributio i Wikipedia also follows the strethed expoetial distributio, the the parameter would be muh smaller tha that of best aswer i our study (.9). Whe is small, we have y log y, ad Equatio beomes power law. Thus, the reported power law distributio of Wikipedia author otributio [] a be explaied. For the emergig miroblog OSNs, suh as Twitter (http: //twitter.om/), the user partiipatios are pervasive as the effort for partiipatig is dereasig i geeral. Based o our study, we ojeture that the SE distributio i suh OSNs should beome flatter as the otributios of ormal users beome domiat i the etwork. Our study suggests that the SE distributio a more aurately reflet idividual user otributios i these OSNs (ad potetially all kowledge-sharig OSNs), whih is sigifiatly differet from the power law distributios that hold for other properties of soial etworks, suh as user s olie oetios i IM ad etworks ad i-boud degree of blog etworks. These pheomea are aused by the aggregatio effet of multiple users, whih a be explaied by the rih-get-riher or preferetial attahmet model []. However, for the ativity of idividual users, the lak of aggregated rih-get-riher effet implies power law aot hold, iludig its variats suh as the power law with expoetial utoff model. The distributio of idividual user otributio is the buildig blok to model more omplex soial etwork pheomea. Although models have bee proposed to desribe how user liks are reated i soial etworks ad how the user etworks evolve with time, the proess of user lik iitializatio

9 durig the evolutio is ofte oversimplified, as we metioed i Setio.. The strethed expoetial model a provide i-depth uderstadig o these soial etwork pheomea.. Disussio: UGC produtio vs. UGC osumptio Although we have ot aalyzed the lik rates of UGC objets i OSNs i this work, a study of Iteret media aess patters has show that the referee rak distributio of objets i Iteret media systems, iludig viral video soial etworks suh as YouTube, follows the strethed expoetial distributio []. I otrast to UGC reatio i soial etworks, whih is to produe otet, a user request i video soial etworks is to osume otet. For user requests i a video system, the streth fator represets the media file size of a objet or the average legth of a objet that users view, i.e., the amout of gai oe obtais. The larger the file size (measured by the legth viewed) is, the greater the streth fator would be. For user otributios i a soial etwork, the streth fator represets the quality of a UGC objet or the effort to reate a objet. The more efforts to reate a objet we make for the higher quality of the reated objet, the smaller the streth fator would be. What is the relatioship betwee UGC reatio ad UGC osumptio i a soial etwork? Why some soial etworks are suessful, with high user populatio ad high quality otet, some are ot? Ca we predit the page views or traffi volume of a soial etwork, with a few properties of UGC reatio patters ad osumptio patters i the etwork? A deeper uderstadig of user behavior patters i OSNs a help us uderstad the drivig fore i these etworks, desig effetive partiipatio mehaisms for soial appliatios, ad provide effiiet resoure maagemet for uderlyig supportig systems.. CONCLUSION Tehology advaemets have brought up may OSNs o the Iteret. For kowledge-sharig orieted OSNs, the user ativities ad otributios are ritial. I this work, we have extesively aalyzed user ativities ad otributios i three large OSNs ad have revealed several ew fidigs that are differet from or otraditig to ommo assumptios. I partiular, the user lifetime i these OSNs does ot follow expoetial distributios, ad the user otributio does ot follow power law distributios, but strethed expoetial. Furthermore, differet types of UGC otet have differet harateristis uder the strethed expoetial model. Our results provide timely isights for the urret soial etwork idustry ad researh ommuities, ad lay out a solid foudatio to guide the desig, modelig, ad simulatio of OSNs with differet properties ad sales. Akowledgmets This work has bee supported i part by U.S. NSF uder grats CNS-9, CNS-9, CNS-, ad CNS-79, ad by U.S. AFOSR uder grat FA We appreiate eouragemet ad ostrutive ommets from Nam Nguye ad aoymous referees. 7. REFERENCES [] L. Adami ad N. Glae. The politial blogsphere ad the U.S. eletio: Divided they blog. 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