FINDING IMPORTANT NODES IN SOCIAL NETWORKS BASED ON MODIFIED PAGERANK
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1 FINDING IMPORTANT NODES IN SOCIAL NETWORKS BASED ON MODIFIED PAGERANK L-qng Qu, Yong-quan Lang 2, Jng-Chen 3, 2 College of Informaton Scence and Technology, Shandong Unversty of Scence and Technology, Qngdao, Chna 3 Shandong labor vocatonal and techncal college Jnan, Chna lqngqu2005@26.com, lyq@sdust.edu.cn 2 wfchenj@26.com 3 ABSTRACT Important nodes are ndvduals who have huge nfluence on socal network. Fndng mportant nodes n socal networks s of great sgnfcance for research on the structure of the socal networks. Based on the core dea of Pagerank, a new rankng method s proposed by consderng the lnk smlarty between the nodes. The key concept of the method s the use of the lnk vector whch records the contact tmes between nodes. Then the lnk smlarty s computed based on the vectors through the smlarty functon. The proposed method ncorporates the lnk smlarty nto orgnal Pagerank. The experment results show that the proposed method can get better performance. KEYWORDS socal networks, Pagerank, lnk smlarty. INTRODUCTION In modern socety, socal networks play an mportant role n a quckly changng world, and more and more people prefer to obtan nformaton from socal networks. Ths explans the ncreasng nterest n socal networks analyss whch examnes topology of a network n order to fnd nterestng structure wthn t. Recent works have ponted that some very actve nodes have huge mpacts on other nodes []. Therefore, the problem of how to approprately fnd mportant nodes n socal networks among the huge nodes becomes an mportant ssue. Pagerank[2,3] s a well known method for dentfyng authortatve pages n a hyperlnk network of web pages. Pagerank reles on the democratc nature of the web by usng ts topology as an ndcator of the value to be attached to any page. Pagerank s so useful that we can also apply t to socal networks n that the mutual relatonshp n socal networks can be structured as lnks to the mcroblogs, and nodes can also be regarded as webstes n Pagerank algorthm [4]. In the paper, we present a new mportance rankng method based on the modfed Pagerank to fnd the mportant nodes n socal networks. In other words, the proposed method s derves from Davd C. Wyld et al. (Eds) : CST, ITCS, JSE, SIP, ARIA, DMS pp , 204. CS & IT-CSCP 204 DOI : 0.52/cst
2 40 Computer Scence & Informaton Technology (CS & IT) Pagerank by consderng the lnk smlarty whch measures the smlarty between the nodes. The paper s organzed as follows. In secton 2 we descrbe our generalzaton of new measurement, and the expermental results together wth the expermental settngs are gven n secton 3. At last we conclude the paper by summarzng our fndngs n secton PROPOSED METHOD In the secton, we propose a new method to fnd mportant nodes based on modfed Pagerank, by consderng the lnk smlarty. We ntroduce the modfed Pagerank model n secton 2., and then we analyze the mportance of nodes usng the model n secton Modfed Pagerank The core dea of Pagerank s that of ntroducng a noton of page authorty. In pagerank, the authorty remnds the noton of ctaton n the scentfc lterature. In partcular, the authorty of a page p depends on the number of ncomng hyperlnks and on the authorty of the page q whch ctes p wth a forward lnk. Moreover, selectve ctatons from q to p are assumed to provde more contrbuton to the value of p than unform ctatons. Therefore, the Pagerank value PR p of p s computed by takng nto account the set of pages pa[ p ] pontng to p.the Pagerank value PR p s defned as follows: PRq PRp = ( d) + d () h q pa[ p] q Here d (0,) s a dumpng factor whch corresponds to the probablty wth whch a surfer jumps to a page pcked unformly at random. The qualty of the lnks, as measured by Pagerank, s a good choce for rankng nodes but we thnk there are some other features that can ncorporate the actvty of the node. We propose to ncorporate the features va the lnk smlarty takng nto account contact tmes of the node. The dea behnd s that the node has hgher smlarty must be przed wth a hgher value. Our man dea conssts n constructng the lnk vector that records the contact tmes of the nodes, defnng a lnk smlarty functon to measure the smlarty of the nodes accordng to the lnk vector, and then reconstructng Pagerank model by consderng the lnk smlarty. These deas are a work n progress. Defnton. For node v, ts lnk vector s defned as: V = { t, t, L, t, t, L, t } (2) + n Where tm (0 m n) s the contact tmes of v and v m. Defnton 2. For node v and v j, the lnk smlarty s defned as:
3 Computer Scence & Informaton Technology (CS & IT) 4 ur uur Smlarty( V, V ) = V V = j j n V m m= V jm n n 2 2 Vm V jm m= m= (3) Obvously, the lnk smlarty measures are functons that take two lnk vectors as arguments and compute a real value n the nterval [0..], the value means that the two nodes are closely related whle the value 0 means the nodes are qute dfferent. Defnton 3. For node v, ts modfed Pagerank value s defned : PRv Smlarty( V, ) j V j PRv = ( d) + d (4) h v j pa[ v ] v j Here pa[ v ] s the set of nodes whch pont to v, and the dump factor d s set to 0.5 n our experments. In the Modfed Pagerank, the lnk smlarty of the nodes s taken nto account, whch s a postve ndcator to modfy the orgnal Pagerank(see Equaton ). 2.2 Node Analyss based on modfed Pagerank The node analyss based on modfed Pagerank s composed of 3 steps as follows: Step: read network as graph; Step2: computer modfed Pagerank value accordng to Equaton 4; Step3: obtan node modfed Pagerank value lst. From above steps, we can see that a bt change s made to the orgnal Pagerank by addng the lnk smlarty ndcator. The modfed Pagerank assumes that the ntal Pagerank values of all nodes are the same. Frstly, we calculate the frst teratve rankng of each node based on the ntal Pagerank values, and then calculate the second rank accordng to the frst teraton. The process contnues untl the termnaton condton s satsfed. At last the Pagerank estmator converges to ts practcal value, whch has proven no matter what the ntal value s. The whole processng s mplemented wthout manual nterventon. 3. EXPERIMENTS In the followng, we use several dfferent networks to study the performance of our generalzaton of novel algorthm for detectng local communty structure. 3. Frst Experment We start wth the frst synthetc dataset, whch s shown as Fgure, to llustrate the process of the proposed method n detal. The network contans 5 nodes, and the contact tmes are assocated
4 42 Computer Scence & Informaton Technology (CS & IT) wth correspondng edges. Fgure. A smple network of 5 nodes and 8 edges. So the mutual relatonshp matrx can be produced as brefly shown n Table. Table. Mutual relatonshp matrx, A. V V2 V3 V4 V5 V 2 2 V2 2 0 V3 2 0 V4 0 V5 0 aj Parameters n the matrx s defned as the contact tmes between the nodes. Then the lnk vectors are: V = {2, 2,,}, V 2 = {2,, 0,}, V 3 = {2,,, 0}, V 4 = {, 0,,}, V 5 = {,, 0,}.Thereby, the lnk smlarty can be computed as: 2* 2 + 2*+ *0 + * Smlarty( V, V 2) = = * The process contnues untl we get the total lnk smlarty of the network. The lnk smlarty matrx s shown as follows: Table2. The lnk smlarty matrx,b. V V2 V3 V4 V5 V V V V V
5 Computer Scence & Informaton Technology (CS & IT) 43 Then the modfed Pagerank can be computed accordng to Equaton 4, and we get the followng Pagerank values: Table3. The modfed Pagerank Values. Value V 0.6 V V3 0.0 V V Second Experment Secondly, we apply our modfed Pagerank method to one small network, whch s the muchdscussed karate club network of frendshps between 34 members of a karate club at a US unversty, assembled by Zachary [5] by drect observaton of the club s members. Ths network s of partcular nterest because the club splt n two durng the course of Zachary s observatons as a result of an nternal dspute between the drector and the coach. In other words the network can be classfed nto two communtes-one s center s the drector, the other s center s the coach. We select degree centralty and PageRank algorthm as baselne methods, whch be dentfed as degree and PageRank respectvely. And our proposed modfed Pagerank method s dentfed as M-Pagerank.Table4 shows the result of the experment. We select the nodes n the top 0 accordng to dfferent methods. Table4. The comparson of dfferent methods degree Node ID PageRank Node ID M-Pagerank Node ID From the above table, we can see that three methods appear to have many common results. However, degree can not dstngush nodes because some nodes have the equal value. For example, node 32 and node 4 have the common value accordng to degree method, whch shows that degree method can not dstngush nodes well. M-Pagerank performs better than Pagerank n that M-Pagerank consders the lnk smlarty of the nodes. For example, node 3 s on the boundary of two communtes, whch has much connecton between the two communtes.
6 44 Computer Scence & Informaton Technology (CS & IT) Accordng to M-Pagerank, node 3 s mportant than node 24 obvously. However, Pagerank rank node 24 hgher than node 3, whch s not reasonable. 4. CONCLUSION In the paper, we have shown a new method to fnd mportant nodes n socal works based on modfed Pagerank. The method s capable of ncorporate the lnk smlarty of the nodes va the lnk vector. The fnal goal for ths model s to ncorporate some features nto orgnal Pagerank. The proposed method enables a new way of rankng the nodes n socal works. We have analyzed the experment results usng test networks. In our future work, we wll further dscuss how to acheve better performance to detect mportance nodes. ACKNOWLEDGEMENT Ths paper s supported by Natonal Scence Foundaton for Post-doctoral Scentsts of Chna under grant 203M54938, and Shandong Provnce Postdoctoral specal funds for nnovatve projects of Chna under grant REFERENCES [] Khorasgan RR, Chen J, Zaane OR.Top leaders communty detecton approach n nformaton networks. KDD 200, -9. [2] Brn S, Page L. The anatomy of a large-scale hypertextual web search engne. WWW7, 998. [3] Banchn M, Gor M, Scarsell F.Insde Pagerank. ACM transactons on nternet technology, 2006, [4] Abbass Z, Mnokn VS. A recommender system based on local random walks and spectral methods. 9th Web KDD and st SNA-KDD 2007 workshop on web mnng and socal network anayss,2007,02-08 [5] Zachary WW. An nformaton flow model for conflct and fsson n small groups, Journal of anthropologcal Research, 977, 33:
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