Abstract
Networks have attracted a great deal of attention the last decade, and play an important role in various scientific disciplines. Ranking nodes in such networks, based on for example PageRank or eigenvector centrality, remains a hot topic. Not only does this have applications in ranking web pages, it also allows peer-to-peer systems to have effective notions of trust and reputation and enables analyses of various (social) networks. Negative links however, confer distrust or dislike as opposed to positive links, and are usually not taken into account. In this paper we propose a ranking method we call exponential ranking, which allows for negative links in the network. We show convergence of the method, and demonstrate that it takes into account negative links effectively.
This research was funded by “Actions de recherche concertes ”Large Graphs and Networks” of the “Communauté Française de Belgique” and from the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office.
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References
Freeman, L.: A set of measures of centrality based on betweenness. Sociometry 40(1), 35–41 (1977)
Freeman, L.: Centrality in social networks conceptual clarification. Soc. Networks 1, 215–239 (1979)
Bonacich, P.: Some unique properties of eigenvector centrality. Soc. Networks 29, 555–564 (2007)
Bonacich, P.: Factoring and weighting approaches to status scores and clique identification. J. Math. Sociol. 2, 113–120 (1972)
Watts, D.J.: A simple model of global cascades on random networks. Proc. Nat. Acad. Sci. USA 99(9), 5766–5771 (2002)
De, P., Singh, A., Wong, T., Yacoub, W.: Sexual network analysis of a gonorrhoea outbreak. Sex Transm. Infect. 80, 280–285 (2004)
Christley, R., Pinchbeck, G., Bowers, R.: Infection in social networks: using network analysis to identify high-risk individuals. Am. J. Epidemiol. 162(10), 1024–1031 (2005)
Perra, N., Fortunato, S.: Spectral centrality measures in complex networks. Phys. Rev. E 78(3), 036107+ (2008)
Kleinberg, J.: Authoritative sources in a hyperlinked environment. J. ACM 46(5), 604–632 (1999)
Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Comput. Networks ISDN 30, 107–117 (1998)
Kamvar, S.D., Schlosser, M.T., Garcia-Molina, H.: The eigentrust algorithm for reputation management in p2p networks. In: Proc. 12th Int. Conf. on WWW, pp. 640–651 (2003)
Abrams, Z., McGrew, R., Plotkin, S.: Keeping peers honest in eigentrust. In: 2nd Workshop on Eco. of P2P Syst. (2004)
Resnick, P., Zeckhauser, R., Swanson, J., Lockwood, K.: The value of reputation on ebay: A controlled experiment. Exp. Econ. 9(2), 79–101 (2006)
Massa, P., Hayes, C.: Page-reRank: using trusted links to re-rank authority. In: Proc. IEEE/WIC/ACM Int. Conf. on Web Int., pp. 614–617 (2005)
Massa, P., Avesani, P.: Controversial users demand local trust metrics: An experimental study on epinions.com community. In: Proc. of the Nat. Conf. on Artif. Int., vol. 20(1), pp. 121–126 (2005)
Szell, M., Lambiotte, R., Thurner, S.: Trade, conflict and sentiments: Multi-relational organization of large-scale social networks. arXiv:1003.5137 (2010)
Maoz, Z., Terris, L.G., Kuperman, R.D., Talmud, I.: What is the enemy of my enemy? causes and consequences of imbalanced international relations, 1816–2001. J. Polit. 69(1), 100–115 (2008)
De Kerchove, C., Van Dooren, P.: The PageTrust algorithm: how to rank web pages when negative links are allowed. In: Proc. SIAM Int. Conf. on Data Mining, pp. 346–352 (2008)
Guha, R., Kumar, R., Raghavan, P., Tomkins, A.: Propagation of trust and distrust. In: Proc. 13th Int. Conf. on WWW, pp. 403–412 (2004)
Harary, F.: On the notion of balance of a signed graph. Michigan Math. J. 2, 143–146 (1953)
Cartwright, D., Harary, F.: On the coloring of signed graphs. Elemente der Mathematik 23, 85–89 (1968)
Antal, T., Krapivsky, P.L., Redner, S.: Dynamics of social balance on networks. Phys. Rev. E 72(3), 036121+ (2005)
Traag, V.A., Bruggeman, J.: Community detection in networks with positive and negative links. Phys. Rev. E 80(3), 36115 (2009)
Sarwar, B., Karypis, G., Konstan, J.: Item-based collaborative filtering recommendation algorithms. In: Proc. 10th Int. Conf. on WWW, pp. 285–295 (2001)
Leskovec, J., Huttenlocher, D., Kleinberg, J.M.: Predicting positive and negative links in online social networks. In: Proc. 19th Int. Conf. on WWW (2010)
Anderson, S.P., De Palma, A., Thisse, J.-C.: Discrete choice theory of product differentiation. MIT, Cambridge (1992)
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Traag, V.A., Nesterov, Y.E., Van Dooren, P. (2010). Exponential Ranking: Taking into Account Negative Links. In: Bolc, L., Makowski, M., Wierzbicki, A. (eds) Social Informatics. SocInfo 2010. Lecture Notes in Computer Science, vol 6430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16567-2_14
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DOI: https://doi.org/10.1007/978-3-642-16567-2_14
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