METHOD FOR DETECTING KEY NODES WHO OCCUPY STRUCTURAL HOLES IN SOCIAL NETWORK SITES

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1 Assocaton for Informaton Systems AIS Electronc Lbrary (AISeL) PACIS 2016 Proceedngs Pacfc Asa Conference on Informaton Systems (PACIS) Summer METHOD FOR DETECTING KEY NODES WHO OCCUPY STRUCTURAL HOLES IN SOCIAL NETWORK SITES Ltng Dng Behang Unversty, Jun Wang Behang Unversty,, We We Behang Unversty, Follow ths and addtonal works at: Recommended Ctaton Dng, Ltng; Wang, Jun; and We, We, "METHOD FOR DETECTING KEY NODES WHO OCCUPY STRUCTURAL HOLES IN SOCIAL NETWORK SITES" (2016). PACIS 2016 Proceedngs Ths materal s brought to you by the Pacfc Asa Conference on Informaton Systems (PACIS) at AIS Electronc Lbrary (AISeL). It has been accepted for ncluson n PACIS 2016 Proceedngs by an authorzed admnstrator of AIS Electronc Lbrary (AISeL). For more nformaton, please contact elbrary@asnet.org.

2 METHOD FOR DETECTING KEY NODES WHO OCCUPY STRUCTURAL HOLES IN SOCIAL NETWORK SITES Ltng Dng, Department of Informaton Systems, Behang Unversty, Beng, Chna, Jun Wang, Department of Informaton Systems, Behang Unversty, Beng, Chna, We We, Department of Informaton Systems, Behang Unversty, Beng, Chna, Abstract It s sgnfcantly meanngful for mprovng nformaton transmsson n socal network ste(sns) to detect the most nfluental nodes. The key nodes who occupy structural holes are easer to acqure nformaton benefts and control benefts from ther relatonshp network. Ths study summarzes the exstng structural holes measurng methods based on Burt s structural holes theory, and provdes a new mproved method accordng to the features of SNS, whch consders the degree of nodes and the topologcal structure of ther neghbor nodes. In addton, to evaluate the accuracy of those measurng methods, the susceptble-nfected-recovered(sir) model s used to smulate experment n four real data sets of socal network. The expermental result shows that our method has a better accuracy and applcablty. Ths paper comes up wth a new dea and method for detectng key nodes who occupy structural holes n SNS. Keywords: structural holes, key nodes, socal network, nformaton transmsson.

3 1 INTRODUCTION Wth the development of SNS and vrtual communty, how to detect key nodes attracts a wde spread attenton. Those key nodes play very mportant roles n whether promotng the actveness of socal networks users or nformaton transmsson. The methods of detectng key nodes can be dvded nto 3 knds roughly: system scence analyss method, the nformaton search analyss method and the socal network analyss method (Newman, 2003), of whch the system scence analyss method measures the mportance of nodes through computng the damage degree of network after detectng the nodes; The most representatve nformaton search analyss methods are PageRank (Page, 1999) and HITS (Klenberg, 1999). Besdes, the socal network analyss method s more general and more sutable for the analyss of bg data n complex networks. The term Socal networks was used by the Brtsh anthropology Brown at the earlest (Brown, 1952). And ts vewpont attracted a wde attenton by the academa n 60-70s of 20th century. The socal network analyss methods measure network structure of the ego networks or the whole networks based on node and relatonshp of networks, of whch mportant measurement ndexes nclude degree, densty, centralty, brdge, betweenness and so on (Newman, 2010). The most famous socal network structure theores are weak tes theory (Granovetter, 1973) and structural holes theory (Burt, 1992). The two theores are relevant, but weak tes theory focuses on the strength of the relatonshp. The occupants of structural holes n the socal networks can get more opportuntes, ncludng nformaton benefts and control benefts (Burt, 2005). Detectng key nodes who occupy structural holes has a gudng sgnfcance on enhancng knowledge transmsson of SNS. Recently, structural holes theory has attracted wdely attenton. However, t s usually used to analyze relatonshp structure of enterprse employees and enterprse resources rather than relatonshp networks of SNS. Thus, ths paper summarzes the exstng structural holes measurng methods, and provdes a new mproved method accordng to the features of SNS, and also evaluates measurng method and analyzes the expermental results through the actual socal network data sets. The paper s organzed as follows: the next secton dscusses the research background, Secton 3 presents the mproved method of detectng key nodes who occupy structural holes, and secton 4 descrbes the data sets and the evaluaton methodology. The emprcal analyss and dscusson are examned n Secton 5. Fnally, we present our conclusons n Secton 6. 2 THEORETICAL BACKGROUND 2.1 The structural holes theory The structural holes theory was mentoned by Ronald Burt n hs book-structural Holes: The Socal Structure of Competton (Burt, 1992). Structural hole descrbes the non-repettve relatonshp between two players of networks. Burt thnks t lke a buffer, an nsulator n an electrc crcut (Burt, Klduff & Tassell, 2013). The strong tes of socal networks mean the lack of structural holes. Burt consders socal network s a knd of socal captal. The players who access to structural holes possess more opportuntes and valuable nformaton, and thus gan compettve advantages (Burt, 2015). Wth the development of the theory, some measurement ndexes of structural holes are mentoned by Burt, whch nclude Constrant (CS), Herarchy (HA), Effectve Sze(ES) and Effcent (EC) (Burt, 2004). In addton, betweenness centralty (BC) mentoned by Freeman (Freeman, 1977) and PageRank are also used to research the nfluence of nodes n socal networks (Brn & Page, 1998). Su and Song (2015) also came up wth a method based on the local centrcty of the neghbourhood. Lou and Tang (2013) dscovered two algorthms to detect the structural holes n the large-scale socal networks based on the nformaton flow theory and mnmal cut theory. As we can see, the measurement ndexes of structural holes have been wdely dscussed recently. However, n the related research, enterprse employees were usually regarded as the research obects, Burt also encouraged the rch network data n vrtual worlds to be used for better understandng networks n the real world (Burt, 2014). Fndng the key nodes based on

4 structural holes theory n SNS s a new research dea. But the relatonshp among the dfferent measurng methods and ther applcaton stll need further research. 2.2 The exstng measurng methods of key nodes who occupy structural holes We summarze 7 exstng measurng methods n table 1. Table 1. The exstng measurng methods of key nodes who occupy structural holes Proposers Name Computng methods Bref ntroducton It expresses the rato of nonredundant relaton of the player s networks. Effectve and are the neghbour Sze ES (1 Pqm q ), q, nodes of. q (ES) s the redundancy Burt Freeman Page Su & Song Effcency (EC) Constrant (CS) Herarchy (HA) Betweenness Centralty (BC) PageRank (PR) N-Burt (NB) HI ES EC n P Z Z q q C ( P P P ) q q q 2 q Pm q q q of node and. It reflects the rato of effectve sze to actual sze. It shows the extent to whch a player s network tme and energy are concentrated n others. s the constrant of to C. Z s the relatonshp C C, strength between and. s the rado of the nvestment of to to ts total network nvestment. C C C ln C The Coleman-Thel nequalty ndex s used to N N Nln N descrbe the herarchy. BC PR P d Q P 1 n It reflects the control degree to network resources of node (Freeman, 1979). st 2 n n 1 st gst P PR P v L P k w v 1 d N Qv Q P The core part of the search rankng technology of Google. Q( ) s the sum of degree neghbor nodes of. kw ( ) s the degree of node w. And s the set of neghbour nodes of. The C s the same as Burt s Constrant.

5 3 THE IMPROVED MEASURING METHOD OF KEY NODES WHO OCCUPY STRUCTURAL HOLES IN SNS The above measurng methods all have some applcablty. But the measurement ndexes of structural holes mentoned by Burt only consder the approxmal nodes, and betweenness centralty would be computed for the mmedate network around a person, whch maybe not be accurate n the large-scale SNS. Combng wth the features of relatonshp networks n SNS, we come up wth a new method to detect the key nodes who occupy structural holes, whch s descrbed as follow n detal. 3.1 V-Constrant (VC) The most mportant ndex n the measurement ndexes of structural holes mentoned by Burt s Constrant. However, Burt usually detects structural holes of the relatonshp networks n enterprses, and assumes one player spends hmself/herself tme and energy on the players who have a drect connecton wth hs/her. Nevertheless, n the SNS, the frendshp means a strong te between two nodes. Thanks to the prevalence of Internet and socal software, t s easy for a user to come nto contact wth other user nodes takng advantage of hs/her frends, and then spend hs/her tme and energy on those user nodes. Take Facebook or Twtter as an example, there are two users who are not frends or don t follow each other n a SNS. But a user can browse to the other user's nformaton easly through hs/her frends shared or forwarded nformaton. Those nvestments of tme and energy should also belong to the nvestment of users spend on ther socal networks. G A B H L F E D C The fgure Burt used to descrbe how to calculate Constrant M Fgure 1. Computng the constrant As we can see from fgure 1, the dashed area s the fgure Burt used to descrbe how to calculate Constrant. Because node E and F have the same neghbour node A wth the purple node. Accordng 2 to the formula of Constrant, CE CF (1/ 6 (1/ 6) (1/ 4)) That s to say, node spends the same tme and energy on node E and F. If node E and F connect to a dfferent number of nodes, t s convenent for node to access the adacent node (G, H, L, M ) of node E and F. Specfcally, when F has more adacent nodes than E, and those adacent nodes don t have relaton wth node and node F are more lkely to share new thngs and nformaton to node so that more tme and energy mantanng relatonshp wth node F. It s a pty that those stuatons cannot be showed n Burt s Constrant. wll spend Therefore, 1, 2 are used to reflect the proporton of users nvestment on ther drect relatons and ndrect relatons s s used to descrbe the nvestment proporton of to hs/her total nvestment n the socal networks for mantanng the relatonshp wth, whch s defned as follow: s p p R (1) 1 2

6 R reflects the rato of the numbers of frends of to the all numbers of frends of adacent nodes of. Those numbers of frends are exclusve of and the common adacent nodes of and F, whch s computed through the ndrect nvestment proporton Here k( ) s the degree of node, and n s the set of neghbour nodes of node. Then, Where q s the common adacent nodes of and. We can survey the users of SNS to get the value of s s q q q,. That s: L k n (2) means the number of common adacent nodes of R L L v and (3) v 2 C s sqsq, q (4) q 1 and typcal users are nvestgated to calculate the average value of 4 SIMULATION AND EXPERIMENT 4.1 Data sets 2. Samplng survey s used. A part of the 1 and 2. To evaluate those several measurng methods, we chose 4 real socal networks to do smulaton experment. The 4 data sets are Zachary's karate club (Zachary, 1977), Dolphn socal networks (Lusseau et al, 2003), coauthorshps n network scence (Of whch the bggest connected subset, called Netscence ) (Newman, 2006) and a connected subset of Twtter user relatonshp networks (Hopcroft, Lou & Tang, 2011). We collected the frst three data sets from the webste: and the last one s from The basc statstcal characterstcs of networks are shown n table 2. Table 2. The basc statstcal characterstcs of networks Name Nodes Edges Average degree Average path length Karate Dolphns Netscence Twtter The evaluaton methodology We use pearson s correlaton coeffcent to analyze the correlaton of the results of those dfferent measurng methods. Besdes, SIR model s usually used to research the nformaton transmsson. Accordng to Burt s structural holes theory, the nodes occupy structural holes are those nodes who can nfluence the.

7 nformaton transmsson of socal networks. Thus, we choose SIR model to smulate the process of nformaton transmsson (Anderson & Mary, 1992; Dekmann & Heesterbeek, 2000; Pastor-Satorrasr, 2001). There are 3 states of SIR model: the state of S (susceptble), I(nfected) and R(recovered). We set one node as the ntal nfected node, ts neghbour nodes can be nfected n a probablty of, and the nfected nodes can be changed to the state of recovered n a probablty of. After a certan tme t, the total number of nodes n state I and R s used to descrbe the actual transmsson capacty of the node. We also sort the actual transmsson capacty of nodes, and have a comparson wth the orderng results of methods of measurng methods of key nodes who occupy structural holes. Kendall tau rank correlaton coeffcent s used to evaluate the valdty of the orderng results (Knght, 1966). 5 THE EXPERIMENTAL RESULTS AND ANALYSIS 5.1 The correlaton analyss of the dfferent measurng methods We evaluate the correlaton of measurng methods based on pearson s correlaton coeffcent as we mentoned n secton 4.2. Take the data set of Twtter as an example, the results of correlaton of measurng methods are shown n table 3. The smlar results are obtaned from the rest 3 data sets. In the method of VC, we set ω 1 = 0.9, and ω 2 = 0.1. Table 3. The results of correlaton of measurng methods of key nodes who occupy structural holes ES EC CS HA BC NB VC PR ES ** ** ** ** **.985 ** EC *.451 ** * * CS * **.926 **.994 ** ** HA * BC ** **.924 ** NB ** ** VC ** PR The smulaton experment analyss of SIR model 2 We set the transmsson tme t 10, the threshold value of nfecton rate ~ k / k. The actual nfecton rate should slghtly bgger than the threshold value so that the nformaton can transmt normally. The recovery rate =0.01. We repeat the experment 100 tmes n term of each node, after that we get the average value of the number of nodes n state I and R, whch s recorded as AT. Then Kendall tau rank correlaton coeffcent s used to calculate the correlaton of orderng results. Fgure 3 shows the results of pearson s correlaton coeffcent of measurng methods and AT (Due to lmted space, only the tow results of Netscence networks are shown here). We only analyze the Constrant, the most representatve measurement ndex of Burt s structural holes theory, and the rest measurng methods. We can see from the results that the actual transmsson capacty has a negatve correlaton wth Constrant, N-Burt and V-Constrant, postve correlaton wth Betweenness Centralty and PageRank. It shows that the several measurng methods can also detect the structural holes nodes whch can mprove the nformaton transmsson. Partcularly, the V-Constrant we came up n ths paper has a more deal result, whch consders the topologcal structure of neghbour nodes, so that can better adapt to the stuaton of Internet and SNS.

8 Fgure 3. The results of pearson s correlaton coeffcent of measurng methods and AT We also compare the experment results of smulaton experment n term of dfferent measurng methods. Due to the lmted space, we only show two of the result fgures n fgure 4. The coordnate of color stands for the actual transmsson capacty of node. It can be seen that the smaller the results of V- Constrant or N-Burt and the bgger the results of PageRank, the AT bgger. Fgure 4. The experment results of smulaton experment n term of dfferent measurng methods Table 4. The results of Kendall tau rank correlaton coeffcent of measurng methods and AT Name (CS, AT) (BC, AT) (NB, AT) (VC, AT) (PR, AT) Karate Dolphns Netscence Twtter Table 4 shows the results of Kendall tau rank correlaton coeffcent. The second column s the nfecton rate we set for the networks. The bgger the absolute value of results of Kendall tau rank correlaton coeffcent s, the rankng results of measurng methods and the actual transmsson ablty are closer. Table 4 reflects that N-Burt and V-Constrant have the good accuracy of orderng results.

9 What s more, to llustrate the real value of several measurng methods, we statstcs the top-5 key nodes occupy structural holes n Netscence data sets n term of N-Burt and V-Constrant, whch have a better performance n the above analyss. As we can see n the table 5, the frst column s the names of authors, column 2 and 3 s the rankng and the last column s the poston Summary of authors. Name Table 5. The top-5 key nodes occupy structural holes n Netscence data sets Rankng NB VC Ttle M. E. J. Newman 1 1 Dstngushed Professor(Unversty of Mchgan) A.-L. Barabás 2 2 Hawoong Jeong 3 3 Romualdo Pastor-Satorras Dstngushed Professor (Northeastern Unversty) Drector(Center for Complex Network Research, Northeastern Unversty) Professor(Korea Advanced Insttute of Scence and Technology) 5 4 Assocate Professor(Unverstat Poltècnca de Catalunya) Stefano Boccalett 4 5 Professor(Unversdad de Navarra) Through the two measurng methods, we fnd several promnent scholars n the felds of complex networks, systems engneerng and physcs. Several emprcal studes also have demonstrated structural holes s postvely relate to a seres of ndcators of socal success (Burt, 2004; Podolny & Baron, 1996). It s vsble that N-Burt and V-Constrant have wonderful practcal value, whch can be used to detect key nodes who occupy structural holes advantages n the socal networks. 6 CONCLUSION AND LIMITATION It s of mportant sgnfcance to detect key nodes n the socal networks for mprovng the effcency of nformaton transmsson. Detectng the key nodes and the sequencng problem of key nodes have been the research hotspot n recent years. In our study, we analyze the Burt s structural holes measurement ndexes, summarze the exstng measurng methods, and come up wth a new measurng method that combnes wth the characterstcs of SNS. Through the smulaton experment wth SIR model, we can prove that our measurng method have a better performance and applcablty than others. Compared wth prevous measurng methods, V-Constrant takes the topologcal structure of neghbour nodes nto account. It can gve a gudance for detectng key nodes n SNS and mprovng the users actveness and nformaton transmsson n SNS. For SNS managers, focusng on key users of the webstes can contrbute to knowledge sharng, controllng rumours and so on. Key users who occupy structural holes wll also be pad attenton by advertsng agences to mprove the effect of advertsement. As for what the user characterstcs of those key nodes who occupy structural holes are, and how to mprove nformaton transmsson, s our future research drectons. Besdes, V-Constrant stll need to mprove to deal wth more complex topologcal structure of nodes. Acknowledgement The work descrbed n ths paper was supported by the Natonal Natural Scence Foundaton of Chna under Grant No and No

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