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Comparison of Online Social Relations in Terms of Volume vs. Interaction: A Case Study of Cyworld Hyunwoo Chun Dept. of Computer Science KAIST, Daejeon, Korea Haewoon Kwak Dept. of Computer Science KAIST, Daejeon, Korea Young-Ho Eom Dept. of Physics KAIST, Daejeon, Korea Yong-Yeol Ahn∗ Center for Complex Network Research Boston, U.S.A. Sue Moon Dept. of Computer Science KAIST, Daejeon, Korea Hawoong Jeong Dept. of Physics KA
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  Comparison of Online Social Relations in T erms ofVolume vs. Interaction: A Case Study of Cyworld Hyunwoo Chun Dept. of Computer ScienceKAIST, Daejeon, Korea Kwak Dept. of Computer ScienceKAIST, Daejeon, Korea Eom Dept. of PhysicsKAIST, Daejeon, Korea thinking22@gmail.comYong-Yeol Ahn ∗ Center for Complex NetworkResearchBoston, U.S.A. yongyeol@gmail.comSue Moon Dept. of Computer ScienceKAIST, Daejeon, Korea sbmoon@kaist.eduHawoong Jeong Dept. of PhysicsKAIST, Daejeon, Korea ABSTRACT Online social networking services are among the most popular In-ternet services according to and have become a key fea-ture in many Internet services. Users interact through various fea-tures of online social networking services: making friend relation-ships, sharing their photos, and writing comments. These friend re-lationships are expected to become a key to many other features inweb services, such as recommendation engines, security measures,online search, and personalization issues. However, we have verylimited knowledge on how much interaction actually takes placeoverfriendrelationshipsdeclaredonline. Afriendrelationshiponlymarks the beginning of online interaction.Doestheinteractionbetweenusersfollowthedeclarationoffriendrelationship? Doesauserinteractevenlyorlopsidedlywithfriends?We venture to answer these questions in this work. We construct anetwork from comments written in guestbooks. A node representsa user and a directed edge a comments from a user to another. Wecall this network an activity network  . Previous work on activitynetworks include phone-call networks [34,35] and MSN messen-ger networks [27]. To our best knowledge, this is the first attemptto compare the explicit friend relationship network and implicit ac-tivity network.We have analyzed structural characteristics of the activity net-work and compared them with the friends network. Though theactivity network is weighted and directed, its structure is similar tothe friend relationship network. We report that the in-degree andout-degree distributions are close to each other and the social in-teraction through the guestbook is highly reciprocated. When weconsider only those links in the activity network that are recipro-cated, the degree correlation distribution exhibits much more pro-nounced assortativity than the friends network and places it closeto known social networks. The k-core analysis gives yet another ∗ This work was conducted while Ahn was at KAIST. Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.  IMC’08, October 20–22, 2008, Vouliagmeni, Greece.Copyright 2008 ACM 978-1-60558-334-1/08/10 ...$5.00. corroborating evidence that the friends network deviates from theknown social network and has an unusually large number of highlyconnected cores.We have delved into the weighted and directed nature of the ac-tivity network, and investigated the reciprocity, disparity, and net-work motifs. We also have observed that peer pressure to stay ac-tive online stops building up beyond a certain number of friends.The activity network has shown topological characteristics sim-ilar to the friends network, but thanks to its directed and weightednature, it has allowed us more in-depth analysis of user interaction. Categories and Subject Descriptors J.4 [ Computer Applications ]: Social and behavioral sciences General Terms Human Factors, Measurement Keywords Online social network, Cyworld, Friend relationship, Guestbook log, Degree distribution, Clustering coefficient, Degree correlation,K-core, Reciprocity, Disparity, Network motif  1. INTRODUCTION Online social networking services are among the most popularInternet services according to and have become a keyfeature in many Internet services. Not only online social network-ingservices( e.g. , MyspaceandFacebook)butalsoothermajorweb2.0 services ( e.g. , Flickr,, and YouTube) offer socialnetworking features on their sites. Through various features of on-line social networking services, users establish friend relationships,sharephotos, andwriteshortmessages. Thefriendrelationshiplaysthe foundation for other systems to build upon for recommendationengines, cooperation-based security, online search, and other per-sonalization functions. Understanding friend relationships is thefirst step towards achieving them.A friend relationship is an explicit and static declaration of arelationship. For actual interaction between users, the friend rela-tionship may not be the best representation. The friend relationshiponly marks a beginning of online interaction. Activities, such aslooking at friends’ photos, reading their articles, and leaving com-ments on their guestbooks, follow once the friend relationship isestablished. Macroscopically, the number of users, the number of  57  daily visitors, and page views are the three most basic metrics tomeasure the status of online social networking services (OSNSs) 1 .These metrics compose an overall view of livelihood of an onlinesocial network service itself, but they do not provide any informa-tion about the livelihood of interaction between users.In this paper, we shift the focus regarding analysis of online so-cial networks from a friends network to an activity network  forbetter understanding of online social networks. We construct anactivity network from logs of actual interaction rather than fromdeclared relationships. The two main sets of questions we raise inthis work are: ã Does the friend relationship reflect underlying user interac-tion? Does a user interact only with one’s friends or explorethe social network more widely? If the social interactiondoes not follow the friends network closely or evenly, track-ing user interaction should become a core design feature inany service site. ã How does information flow through the network? Do allusers receive the same attention from their friends? Howoften do they interact? Is the interaction one-way or recip-rocated?We take a top-down approach and begin our analysis with net-work growth. The activity network  built for the present work isdirected and weighted. The direction represents the flow of in-teraction and the weight the amount of interaction. We first look at the numbers of users in the friend and activity networks andcompare their growth over time. We then compare the topologicalcharacteristics–namely, the degree distribution, the clustering co-efficient, and the degree correlation–of the two networks. We usereciprocity, disparity, and network motifs to investigate the activ-ity network’s unique characteristics in the form of a weighted anddirected graph.For our work, we use more than two years of guestbook logsfrom the largest online social networking site in Korea and builda graph from the comments recorded in these logs. The friendsnetworkisacompletesetoffriendrelationships. Accesstothisdataset allows us unique opportunities otherwise not possible, as thefriend lists of some users are often kept private and data collectedby crawling contains unavoidable bias.Previousworkonactivitynetworksincludesphone-callnetworks[34, 35] and MSN messenger networks [27]. Online social net-worksareuniqueinthattheyhavethisreferencenetworkoffriends.To the best of our knowledge, this is the first attempt to compare the explicit  friend relationship network and implicit  activity network.The remainder of this paper is structured as follows. In Section 2wedescribeourguestbooklogsandthefeaturesspecifictoourlogs.In Section 3 we compare the topological characteristics betweenthe friend and activity networks. We then delve further into theweighted and directed aspects of the activity network in Section 4and other activity-related aspects In Section 5. In Section 6 wecompile related work and Section 7 concludes with a discussion onfuture work. 2. ACTIVITY IN GUESTBOOK In this section, we describe the social network data we use forthis study. Cyworld, launched in 2001, is the largest online socialnetwork service in Korea. As of October 2007, the number of reg- 1 Ranking sites, such as Alexa, Rankey, and Ranking, use thesemetrics in their web site rankings.istered Cyworld users has surpassed 20 million, which is more thana third of the entire South Korea population 2 . Figure 1: Screen capture of user C’s guestbook When a user joins Cyworld, one is given a homepage (called minihompy ) that contains an avatar, a photo gallery, a public di-ary, a testimonial board, a guestbook, etc. A user can establish  friend  relationships with other users and share information onlywith those established relationships. Users browse through friends’photos and leave comments. They read others’ public diaries andwrite testimonials for those established friends. Some of the fea-tures, such as writing a testimonial and viewing photos, are oftenlimited to only those with established online friend relationships.The owner of the minihompy can choose the buttons or features onone’s minihompy. Some features, such as the profile and the diary,are read-only, while access to other features are owner-configurableexcept for the guestbook. Once the owner includes the guestbook on the minihompy, then it is open to anyone to write, a friend or not.Even a person not registered as a Cyworld user can still visit andwrite a comment on a guestbook. The photo gallery and the bulletinboard can be configured to be writable by visitors, but many userskeep the default setting of write-by-owner-only. The guestbook isthe most used feature in Cyworld where friends and visitors leavea note of greetings to the minihompy owner 3 . We include a screencapture of a typical interaction on a Cyworld guestbook in Figure 1.A comment writer’s name and avatar are displayed along with thecomment.Ahn et al. have analyzed Cyworld’s topological characteristicsof bi-directional friend relationships [2]. Once established, a friend 2 Upon joining, a new user must have its personal identificationnumber (equivalent of U.S.’s social security number) verified. For-eigners have special provisions for membership. All user accountson Cyworld map to real users, unless a user make an illicit use of other people’s personal identification numbers. 3 We were offered logs of comments on the photo gallery and thebulletin board of the same period, but they were far smaller thanguestbook logs. 58  relationship remains rigid regardless of the actual relationship [40].It is an assertion that some relationship existed, currently activeor not. In this work, we delve deeper into the web of social net-working and study the user interaction captured in the guestbook.Unlike a friend relationship, which is bi-directional, a message ona guestbook represents a directional interaction between users. Ona guestbook, people write greetings, recent updates, replies, and soon.We have obtained the complete guestbook logs of Cyworld fromJune 2003 to October 2005 4 . This period is very important in thedevelopment of Cyworld, as the number of users grew exponen-tially from 2 million to 16 million and the friend relationship net-work began to show a sign of densification [2]. In this work we in-vestigate whether the growth in actual user interaction, a key aspectof social networking services, has kept up with the growth in sheersize. Our guestbook log consists of three-tuples: the writer, theguestbook owner, and the time of the guestbook comment. All useridentifiers have been anonymized. As of October 2005 , the num-ber of Cyworld subscribers reached 16 , 146 , 817 . Among those 16 million users, 74 . 6% or 12 , 048 , 186 users have formed friendrelationships with others, and 64 . 8% or 10 , 476 , 604 users havewritten or received a comment on a guestbook at least once dur-ing the period of our guestbook logs. Compared to 381 , 602 , 530 friend relationships, the number of the writer and guestbook ownerpairs is larger: 537 , 970 , 431 . Table 1 summarizes our dataset. Thenumbers in the parentheses exclude messages written by the ownerof the guestbook on one’s own guestbook. We explain more aboutthis type of messages in Section 2.2. Table 1: Summary of Cyworld Guestbook Logs Period 2003.06 ∼ 2005.10# of 3-Tuples 8,423,218,770# of unique writer-owner pairs 537,970,431# of guestbook users 17,788,870Mean # of msg per writer 637 (397)Mean # of msg received per owner 484 (297) 2.1 Growth in Guestbook Activity Figure 2: Cyworld growth in numbers 4 The period of guestbook logs does not match that of the friendsnetwork in [2]. We could not retrieve the friends network from thesame period as the guestbook logs.As the number of Cyworld subscribers grew almost ten times be-tween 2003 and 2005, its guestbook had also seen explosive growthin activity. We plot the number of Cyworld subscribers and therelevant statistics in Figure 2 5 . The top graph represents the totalnumber of subscribers. The next two graphs crisscross each otherin about October 2004. The graph marked with a square representsthe cumulative number of guestbook writers, and that marked witha circle the number of users with friend relationships. The formercould be larger than the latter, because the guestbook is open toanyone. Even if a person has not established a friend relationshipwith the guestbook owner or is not even a registered user of Cy-world, one can still write on a guestbook. The bottom graph repre-sents the number of guestbook writers in that month. The numberof guestbook users was very small at the beginning, but caught upwith the total number of Cyworld users fast. It surpassed the num-ber of users with friend relationships, attesting that it is the mostused feature.However, the monthly statistics of guestbook users started toabate in growth. Here we observe a hint of slow-down in Cyworldgrowth. The slow-down tendency is also observed in the growthrate of the number of guestbooks and messages per writer. Figure 3shows the total number of guestbook comments and the number of user pairs against the number of guestbooks users. Figure 3: Growth in the numbers of guestbooks and messagesversus the number of users The total number of guestbooks that users have written does notincrease very fast after the number of users exceeds 10 million.No social network can sustain an explosive growth forever, and itsgrowth rate must slow down at some point. As Cyworld is lim-ited to Korean-speaking populace of 70 million to 100 million 6 ,the slow-down in growth in around July 2004 or at about 8 mil-lion is markedly interesting. We do not have data from other socialnetworking services, but take a mental note that at about 10% of the target market size the growth slows down. Similar slow-downin growth has been observed in bulletin board systems (BBS) of auniversity as well [17]. In this network, BBS users are connectedthrough message posting like leaving comments in the guestbook.The number of users in BBSs grow exponentially, but the growthrate eventually drops below an exponential rate. The total numberof links and the total weight of BBS networks also grow exponen- 5 The total number of friends and the number of users with friendsin this figure are a courtesy of SK Communications, Inc. 6 Cyworld has opened service in China, Japan, Taiwan, and USA.Each service runs independently and the user based is not shared. 59  tially at the beginning, and then their growth rates slow down sim-ilarly [15]. The starting point of inevitable slow-down in growth isof interest to online social networking service (OSNS) providers, asit marks a transition from a fast-growing phase to a steady growth.Our observation is just one exemplary data point, and we leave thecorrelation between the point of transition and the expected popu-lation of the service for future work. 2.2 Self-Posting in Guestbook When a friend writes a message on a guestbook, the owner of the guestbook often replies in one’s own guestbook, instead of vis-iting the friend’s guestbook and writing there. This activity is cap-tured in our guestbook log as a 3-tuple that has the same writerand owner. We call this tuple a self-post. Self-posts take up abouta third or 38.9% in all posts, and they are evenly distributed overtime. Also 81.8% of users who have written at least once have writ-ten a self-post. For half of the users, a third of messages they wroteare self-posts. Self-posts make up a non-negligible portion and weshould determine how to interpret self-posts before analyzing useractivities of guestbook logs.A self-post serves either of the two purposes: a message forviewing by all others (a notice) or a reply specifically for a pre-ceding message. We cannot distinguish a notice from a reply in theguestbook log, as they both appear as 3-tuples with the same writerand owner. As Cyworld offers two other features, the bulletin boardand the public diary, that both serve a similar purpose for noticesand announcements, we assume most self-posts are replies for thiswork. Figure 4: Self-posts vs messages received In Figure 4 we plot the number of self-posts against the numberof messages received per user. There is a strong positive correla-tion between the two numbers; the Pearson correlation coefficientbetween the two numbers is 0 . 8201 . Most points lie below theline, y = x , and about 95.1% of users’ self-posts are smaller thantheir received messages. We see a small number of points above y = x in the left bottom corner. Our guestbook logs only includecomments between registered users of Cyworld and do not containcomments by non-Cyworld users. Non-Cyworld users can browseminihompies and write on guestbooks, as long as owners of theguestbooks allow it. Non-Cyworld users do not have a user id, andtheir activity is not logged in our data. This explains those pointsabove y = x in the left bottom corner.From above, we conclude that the self-posts represent recipro-cal activity, but face a dilemma because we cannot disambiguatethe actual recipient. For example, a minihomy owner has receivedmessages from users i and j , and writes one self-post a few dayslater. Is the self-post meant for user i , user j , or both? We cannottell from the data we have. However, self-posts are an importantaspect of user activity, and we cannot drop them completely in ouranalysis. In the rest of the paper, we make it explicit whether weinclude self-posts in the analysis or not. 2.3 Activity Network Graph representation of a social network is an apt abstraction of their connected nature and allows us to tap into the rich repositoryof graph and complex network theories. In this section we describehow we represent the user interaction on the guestbook as a graphand define metrics of interaction.In a network of nodes and edges without directions, a node de-gree refers to the total number of edges. For the guestbook activity,we construct a network with weighted and directed edges. We mapa user to a node and a message to a directed edge from a writer toa reader (we refer to a user and a node interchangeably). An edgefrom node i to node j denotes that user i has written a message onuser j ’s guestbook. The weight, w ij , of a directed edge from i to j is the number of messages user i has written to user j . A node in adirected network has two degrees: an in-degree and an out-degree.We often refer to an out-degree in a directed network as the degree,and specify in-degrees when necessary.In a weighted network, a node strength represents the sum of allweights of outgoing edges. The strength of node i with out-degree k is defined as: s i = Σ kj =1 w ij .We call a weighted and directed network constructed from theguestbook log the activity network  . Note that the nodes of the activ-ity network is not a proper subset of that of the friends network, forusers without friend relationships can still write onto one’s guest-book.Self-posts map to a reflexive edge pointing back at the srcinat-ing node itself, and the weight is the number of self-posts. It isreasonable to include self-posts in the strength, as self-posts aremeant for other users. Figure5: CCDFofstrengthanddegreesoftheactivitynetwork In Figure 5 we plot four complementary cumulative distributionfunctions (CCDFs) of the strengths and out-degrees of the activitynetwork; two of them are daily averages of the strength and theout-degree.As our guestbook data is from the period of explosive growth,a large number of users have joined and the time of membership 60
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