An Interest-Oriented Network Evolution Mechanism for Online Communities

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1 An Interest-Orented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng , P.R. Chna Abstract. Onlne communtes nvolve lots of nteractons among members. Those nteractons are usually shown as frend lnks between communty members, and an onlne communty could be seen as a network of members. The structures and propertes of communty network formed are mportant to the nformaton dffuson n communtes. Hence, the network formaton mechansms attract great nterest n recent years. In ths paper, an nterestorented network evoluton mechansm s proposed to study the growth and evoluton of socal network of onlne communtes. Agents n an onlne communty tend to choose those who share smlar nterests wth them to be ther frends. In our model, we defne n dfferent nterest categores; they could refer to sports, moves, musc, lteratures and so on. Each agent has an nterest vector,,..., ) to ndcate ts nterests. ( Keywords: Network evoluton mechansm, Onlne communtes, Socal network, Informaton dffuson, Frendshp network 1. INTRODUCTION In recent years, onlne communtes (.e. Wks, Blogs, Forums, etc) have attracted great nterest and become the mportant knowledge sharng resources. Onlne communty or vrtual communty s a group of people communcatng or nteractng wth each other by means of nformaton technologes, typcally the Internet, rather than n person. In bref, an onlne communty s a knd of computer-supported socal network (CSSN) [1, 2], n whch members and ther frend lnks form socal networks. How to form the structure of an onlne communty from the begnnng? What are the mechansms of network evoluton? Many researchers have put ther efforts on studyng these network evoluton mechansms ever snce the random graph model of Erdos and Reny could not explan some features of network structure. Degree dstrbuton of random graphs follows a Posson law, whereas many emprcal socal networks exhbt power law degree dstrbutons. Watts and Strogatz [3], Barabas and Albert [4] proposed small world and scale-free network evoluton models respectvely. They provded new emergng smulaton technques to nvestgate the dynamcs of a socal network on the evoluton of the network tself overtme.

2 1284 Cahong Sun and Xaopng Yang In 1995, Holland frst brought forward the concept of tag. A tag works lke a flag that dentfes one group of users from another. Holland assumed that arbtrary, evolvng tags could facltate selectve nteractons and thereby be helpful for aggregaton and boundary formaton [5]. In Rolo s work publshed on Nature, they used computer smulaton methods and demonstrated that tag-based mechansm could lead to the emergence of cooperaton even when the agents do not receve recprocty and are unable to observe or remember others actons [6]. In ths paper, we proposed an nterest-orented network evoluton mechansm based on the dea of tag and Schellng Segregaton Model [7]. The model s an agentbased model, n whch communty members are smulated as agents who can decde whether to lnk other agents as ts frends or not, accordng to ther nterest smlartes. The man dea of ths model s that agents n an onlne communty tend to choose those who share smlar nterests wth them or have hgh reputaton value to be ther frends. Agents nterests could be affected by ther frends nterests by beng conform to one another. Ths smulates the trends that agents learn from ther frends. In the proposed model, n dfferent nterest categores are defned; they could refer to sports, moves, musc, lteratures etc. Each agent has an nterest vector (,,..., ) to ndcate ts nterests. If an agent s nterested n nterest category, then If =1, otherwse =0. The more two agents share the same nterest categores, the more the two agents nterests are smlar. The rest of ths paper s organzed as follows: In Secton 2, an nterest-orented network evoluton mechansm s presented to smulate the evoluton of the socal network structures of onlne communtes. Secton 3 dscusses the expermental desgn and demonstrates some smulaton results. Secton 4 concludes ths paper and dscusses future work. 2. AN INTEREST-ORIENTED NETWORK EVOLUTION MECHANISM The nterest-orented network evoluton mechansm smulates the phenomena n real world that people on nternet tend to choose that who share the smlar nterests wth themselves to be ther frends. But usually people have many nterests, how to smulate these nterests and defne the nterest smlarty? We defne n dfferent nterest categores; they could refer to sports, moves, musc, lteratures etc. Each agent has an nterest vector (,,..., ) to ndcate ts nterests. If an agent s nterested n nterest category, then If =1, otherwse =0. In addton, an agent could specfy ts nterest weght for each nterest element as ( w, w,..., w ). The smlarty between agent and j s defned as Equaton (1).

3 An Interest-Orented Network Evoluton Mechansm for Onlne Communtes 1285 n w v h h jh h 1 IS(, j) 1 n (1) h 1 w v Where w, w,..., w ) s the nterest weght vector of agent ( 1 2 n. 0 w 1, for any agent, and h=1,,n. Agent and j may have dfferent nterest h weght vector,.e. w, w,..., w ) ( w, w,..., w ). ( 1 2 n j1 j2 jn Moreover, each agent has a threshold (denoted as T ) whch s the degree of smlarty by whch an agent chooses ts frends. Agents have ther own prvate smlarty tolerance degree. Our mechansm s that an agent randomly selects some agents as ts frend canddates, but only those who have smlarty greater than ts smlarty tolerance threshold wll become ts frends. The proposed nterest-orented network evoluton mechansm follows three rules: Rule 1. Growth of agents: Startng wth a small random network (wth m nodes, 0 and probablty p), and at each tme step, we add m new agents. The nterest vector, weght vector and threshold of the new agent are randomly generated. All agents follow Rule 2 to add ther lnks. Rule 2. Growth of lnks: At every tme step, each new agent selects ts own frend for g ( g 1) tmes. The selecton ncludes two steps: frst, the agent A randomly gets another agent n the network; second, t compares the selected agent s nterests and ts own nterests; f the nterest smlarty s greater than ts threshold ( T A ), then one lnk to the selected agent s added, otherwse the agent wll not add the lnk. Rule 3. Learnng from frend s nterest: At every tme step, an agent who adds a new lnk wll adapt ts own nterest vector accordng to the nterest vector of ts new frend. The agent wll add a new nterest element whch t has no such nterest but ts frend has accordng to ts nterest weghts. h 3. EXPERIMENT DESIGN In our experments, the number of nterests (denotes as k) of each agent follows normal dstrbuton,.e., k N(,1), where n. For an agent wth k nterests, we randomly select k nterests to form ts nterest vector. The more two agents share the same nterest categores, the more the two agents nterests are smlar. The nterest weght vector s used to provde an nterface to specfy the mportance of ts nterest for a member n an onlne communty. To smplfy the smulatons, let all the nterest weghts equal 1, n other words, every nterest category s treated equally by all the agents.

4 1286 Cahong Sun and Xaopng Yang The smlarty threshold T follows the unform dstrbuton wth the range of (0.1, 0.5) f n equals 10. Every agent has ts own smlarty threshold. If n equals 1, then the nterest-orented mechansm s degraded nto the tag-based mechansm proposed n [8], f we do not treat the nterest element as a bnary but a real number n [0,1]. In order to study the effectveness of nterest-orented network evoluton mechansms, we plan to do the followng experments. 3.1 Experment 1 What are the degree dstrbuton, average path length and clusterng coeffcent of the networks generated by the proposed mechansm? Parameters n ths experment are: The number of agents: N=10000 The number of nterest categores: n=2, 5, 10, 15 The mean : =1, 2, 5, 8 Note: the number of nterests (denotes as k) of each agent follows normal dstrbuton: k N(,1). The ntal random network: m =10, p=0.2 0 The number of agents who can gan lnks: m=1, 2, 5, 10 The selecton chance: g=1, 5, , 1000, N Threshold follows the unform dstrbuton wth the range of [0, 0.5], [0.1, 0.5], etc. In ths experment, we study the degree dstrbuton of network by changng n, k, m, and g respectvely. The parameter g denotes the frend search area, parameter m represent the scale of the new agents n each tme step. Degree dstrbuton, average path length and clusterng coeffcent are three mportant propertes researched n socal network: Degree dstrbuton descrbes the probablty dstrbuton of degrees n a network; average path length can descrbe how fast nformaton can travel n a network; and clusterng coeffcent of a network s used to descrbe how closely frends are clustered n a network. 3.2 Experment 2 What wll happen f Rule 3 (learnng from frends tags) s removed from our mechansm? Based on parameters set up n the experment 1, by deletng Rule 3 n the proposed mechansm to examne how the degree dstrbuton, average path length and clusterng coeffcent change. 3.3 Experment 3 What are the dfference on degree dstrbuton, clusterng coeffcent and average path length between emprcal data and networks generated from the nterest-orented mechansm?

5 An Interest-Orented Network Evoluton Mechansm for Onlne Communtes 1287 The man am of experment 3 s to compare the network structure generated from the nterest-orented mechansm and some emprcal networks exstng n real world. 4. CONCLUSIONS AND FUTURE WORK In ths paper, an nterest-orented network evoluton mechansm s presented. The man am of ths mechansm s to generate a hgher-qualty communty n whch frend lnks are more evenly dstrbuted, dstances between members are smaller and members are more closely clustered by nterests. Three experment desgns are gven to study the effectveness of the proposed mechansm. Comparng wth the tag-based mechansm and other network evoluton mechansms, such as preferental attachment [4,9,10], small world model, and the nterest-orented network could have multdmensonal concerns when addng a new lnk. Our future work ncludes: (1) analyzng the expermental results based on the experment desgns proposed n secton 3; (2) studyng the emergent propertes of the mechansm whch combnes nterest-orented mechansm wth preferental attachment mechansm; (3) examnng the nterest weght effects; and (4) consderng the lfe cycle of the agents. We wll examne the effects on frend networks by breakng some frend lnks and ntroducng agents lfe span. REFERENCES 1. B.Wellman, J. Salaff, D. Dmtrova, L. Garton, M. Gula and C. Haythornthwate, Computer Network as Socal Networks: Collaboratve Work, Telework, and Vrtual Communty, Annual Revew of Socology. Volume 22, pp , (1996). 2. L. Garton, C. Haythornthwate and B. Wellman, Studyng Onlne Socal Networks, Journal of Computer Medated Communcaton. Volume 3, Number 1, (1997). 3. D.J. Watts and S.H. Strogatz, Collectve dynamcs of 'small-world' networks, Nature. Volume 393, pp , (1998). 4. A.L. Barabaas and R. Albert, Emergence of scalng n random networks, Scence. Volume 286, pp , (1999). 5. J. Holland, Hdden Order: How Adaptaton Bulds Complexty (Addson Wesley, 1995). 6. R. Rolo, R. Axelrod, and M.D. Cohen, Evoluton of cooperaton wthout recprocty, Nature. Volume 414, pp , (2001). 7. T.C. Schellng, Mcromotves and Macrobehavor (W. W. Norton and Co, 1978), pp C. Sun, Y. Xu and X. Yang, A tag-based network evoluton mechansm for onlne communtes, the thrd nternatonal conference on natural computaton (Forthcomng, 2007). 9. C. Roth, Generalzed preferental attachment: towards realstc socal network models, n Proceedngs of Workshop on Semantc Network Analyss at the ISWC (2005). 10. M. Dell Amco, Hghly-clustered networks wth preferental attachment to close nodes, European Conference on Complex Systems (Oxford, 2006).

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