Vol.6 No (Aug. 2013) Twitter 1,a) , Twitter Twitter Study of Twitter s Follow Mechanism Based on Network

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1 Twitter 1,a) , Twitter Twitter Study of Twitter s Follow Mechanism Based on Network Analysis Akihiro Koide 1,a) Kazumi Saito 1 Kazuhiro Kazama 2 Fujio Toriumi 3 Received: November 3, 2012, Revised: January 25, 2013, Accepted: March 27, 2013 Abstract: In this paper, we explored Twitter s follow mechanism through a network analysis. In order to characterize the salient structure of Twitter s follow network, we first empirically compared it with those of reader and favorite networks form blog and review sites by focusing on their high degree nodes. From this experiment, we observed a relatively large high co-link group whose nodes are mutually connected to each other and some small low co-link groups whose nodes are not mutually connected to each other in Twitter s network. On the other hand, most groups are relatively small high co-link groups such as discussion groups in blog and review sites. Moreover, by analyzing messages tweeted by these group s users, we found that these groups much differ in relation with followers although these groups resemble in content of tweets. Keywords: social network analysis, Twitter, degree, dendrogram, co-link 1. 1 Twitter *1 1 Graduate School of Management and Information of Innovation, University of Shizuoka, Shizuoka , Japan 2 Faculty of Systems Engineering, Wakayama University, Wakayama , Japan 3 Graduate School of Engineering the University of Tokyo, Bunkyo, Tokyo , Japan a) a.koide1988@gmail.com *1 [1] Twitter Facebook *2 mixi *3 SNS Twitter *2 *3 c 2013 Information Processing Society of Japan 164

2 @ Mention Twitter Kwak [10] SNS Mention 2 [2], [3] Twitter 6 2. SNS SNS Adamic SNS [4] SNS [5] SNS mixi [6] [7] SNS SNS mixi [8] Ameba mixi [9] Kwak [10] Huberman 2 [11] Cha [12] Twitter 3. G =(V,E) V = {v 1,v 2,...,v N } E V V N v i V v i A(v i )={v j ;(v i,v j ) E} v i B(v i )={v k ;(v k,v i ) E} Twitter 1 Twitter X Y X Y ,079, ,371,341 TwitterNW 2011 c 2013 Information Processing Society of Japan 165

3 3 7 0:00: :00:00 1,079,986 57,625, Ameba *4 [9]amebloNW Ameba X Y X Y 56,604 1,071, * cosmenw X Y X Y 10 45, , L L = E N(N 1). (1) cr [14] cr = 1 A(v i ) B(v i ). (2) E v i V mixi 1 TwitterNW TwitterNW 6 ameblonw cosmenw 3.3 k% k k *4 *5 1 Table 1 Basic Statistics of each network. TwitterNW ameblonw cosmenw ,938 3, ,616 6,291 1, k% R + (k) k% R (k) R + (k) R (k) Jaccard J(R + (k),r (k)) = R+ (k) R (k) R + (k) R (k). (3) k =1, 2,, 100 k = Jaccard 1 k% k% Jaccard TwitterNW ameblonw 1% 1 cosmenw PageRank HITS PageRank Web [16] Web Web Web Web PageRank HITS c 2013 Information Processing Society of Japan 166

4 Fig. 1 1 Jaccard Jaccard coefficient between set of outdegree nodes and indegree nodes. 2 TwitterNW Jaccard Fig. 2 Jaccard coefficient between degree and ranking index on TwitterNW. [17] Hub Authority Authority Hub PageRank Hub Authority Jaccard PageRank α =0.15 TwitterNW Jaccard 2 OutD InD OutPR PageRank InPR PageRank Hub Hub Authority Authority TwitterNW 1% [15] v i IC(v i ) OC(v i ) IC(v i )= A(v i) B(v i ). A(v i ) (4) OC(v i )= A(v i) B(v i ). B(v i ) (5) A(v i ) B(v i ) 0 (4) (5) C(v i )= 2 1 IC(v + 1 i) OC(v i) = 2 A(v i) B(v i ). (6) A(v i ) B(v i ) [13] 3 TwitterNW TwitterNW Twitter 4 TwitterNW ameblonw c 2013 Information Processing Society of Japan 167

5 Fig. 3 3 Change of co-link ratio focus on outdegree ranking. Fig. 4 4 Change of co-link ratio focus on indegree ranking v i v j A(v i ) 1 0 v i a i A [ ] T A = a 1 a N (7) B [ ] T B = b 1 b N (8) v i v j N n=1 ρ(v i,v j )= a i,n a j,n (9) ρ(v i,v j )= N n=1 a2 i,n N n=1 a2 j,n N n=1 b i,n b j,n N n=1 b2 i,n N n=1 b2 j,n (10) N N D d(v i,v j )= (1 ρ(v i,v j )) (11) G C =(V,E) T [18] (i) G C S T =Ø K (ii) S (v i,v j ) S = S/(v i,v j ) (iii) v j / K(v i ) T (v i,v j ) K(v i )=K(v i ) K(v j ) (iv) S =Ø (ii) (iii) T 1 1 N c 2013 Information Processing Society of Japan 168

6 (a) ameblonw 1000 (b) cosmenw ameblonw cosmenw 1000 Fig. 5 Dendrogram of top1000 nodes on ameblonw and cosmenw. (a) 6 Fig. 6 TwitterNW 1000 Dendrogram of top1000 nodes on TwitterNW. (b) 1000 ameblonw cosmenw (a) ameblonw (b) cosmenw 2 ameblonw cosmenw 6(a) Twitter (b) 7 c 2013 Information Processing Society of Japan 169

7 7 Fig. 7 Distance between nodes on minimum spanning trees. TwitterNW TwitterNW 6(a) 6(b) 6(a) Twitter TwitterNW Fig. 8 Link structure of top1000 indegree nodes. 4 A B C D C D (i) A (ii) B (iii) C A A B (iv) D B A B A B C D TwitterNW 75% 8 A 686 B C D 35% B C 90% D A C 0.75 A 0.90 B D 0.21 B 0.46 B D 5.2 URL 1 URL URL c 2013 Information Processing Society of Japan 170

8 1 [19] A B URL URL A 37% URL B URL 34% A 12% A B URL 3 A B URL A Web B A URL 5.3 Twitter Mention Mention Mention Mention Huberman [11] 1 A B C D 9 8 A B C D A B A C B D 2 C D 36% D 58% A B A C Fig. 9 Conversation structure of top1000 indegree nodes Fig. 10 Information transmission structure of top1000 indegree nodes. Twitter 1 2 A B C D 10 A B D C D 6% B D 5.5 A c 2013 Information Processing Society of Japan 171

9 B Twitter Twitter Twitter Twitter 6. Twitter URL URL Twitter Twitter Twitter NTT [1] 23 (2011) ja/h23/pdf/. [2] Leskovec, J., Adamic, L.A. and Huberman, B.A.: The Dynamics of Viral Marketing, Proc. 7th ACM Conference on Electronic Commerce, pp (2006). [3] Twitter 26 (2012). [4] Adamic, L.A. and Adar, E.: Friends and Neighbors on the Web, Social Networks, Vol.25, No.3, pp (2003). [5] SNS Vol.47, No.9, pp (2006). [6] Vol.47, No.3, pp (2006). [7] SNS mixi Vol.22, No.5, pp (2007). [8] SNS Vol.25, No.1, pp (2010). [9] 2 pp (2006). [10] Kwak, H., Lee, C., Park, H. and Moon, S.: What is Twitter, a Social Network or a News Media?, Proc. 19th International Conference on World Wide Web, pp , ACM (2010). [11] Huberman, B.A., Romero, D.M. and Wu, F.: Social Networks that Matter: Twitter under the Microscope, First Monday, Vol.14, No.1 (2009). [12] Cha, M., Haddadi, H., Benevenuto, F. and Gummadi, K.P.: Measuring User Influence in Twitter: The Million Follower Fallacy, Proc. 4th International Conference on Weblogs and Social Media (2010). [13] Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D. and Alon, U.: Network Motifs: Simple Building Blocks of Complex Networks, Science, Vol.298, No.5594, pp (2002). [14] Ohara, K., Saito, K., Kimura, M. and Motoda, H.: Effect of In/Out-Degree Correlation on Influence Degree of Two Contrasting Information Diffusion Models, Proc International Conference on Social Computing, Behavioral Modeling, and Prediction, pp (2012). c 2013 Information Processing Society of Japan 172

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