Modelling Social Network Sites with PageRank and Social Competences

[EN] In this communication a recent method to classify the users of an SNS into Competitivity groups is recalled. This method is based on the PageRank algorithm. Competitivity groups are sets of nodes that compete among each other to gain PageRank via the personalization vector. Specific features of the SNSs (such as number of friends or activity of the users) can be considered as Social Competences. By means of these Social Competences a node can modify its ranking inside a Competitivity group.This work is supported by Spanish DGI grant MTM2010-18674.Pedroche Sánchez, F. (2011). Modelling Social Network Sites with PageRank and Social Competences. International Journal of Complex Systems in Science. 1(1):65-68. http://hdl.handle.net/10251/46059S65681

On the Localization of the Personalized PageRank of Complex Networks

In this paper new results on personalized PageRank are shown. We consider directed graphs that may contain dangling nodes. The main result presented gives an analytical characterization of all the possible values of the personalized PageRank for any node.We use this result to give a theoretical justification of a recent model that uses the personalized PageRank to classify users of Social Networks Sites. We introduce new concepts concerning competitivity and leadership in complex networks. We also present some theoretical techniques to locate leaders and competitors which are valid for any personalization vector and by using only information related to the adjacency matrix of the graph and the distribution of its dangling nodes

Potentialities and usage of Internet communications: A qualitative and quantitative overview.

Technological innovation is the main responsible of the phenomenon called Internet. This innovative use of the medium accomplishes those concepts and dreams of science fiction's authors. Nevertheless, the new potentialities supplied by this new medium have only partially been analysed until today. Our purpose is to define a qualitative schema to investigate the main usage of Internet potentialities, joined with a quantitative analysis in the main geographic areas paying a special attention to the national and EEC data. The first goal is pursued identifying the better usage of the medium done by some representitives of the main socio-economic categories. These representitives could be chosen in any geographic area and their performances will be investigated, compared and used to define an analysing schema. The second objective is obtained using the best so-called "search engines", since the main characteristic of a site is represented by it's accessibility. Moreover, some cross-section data will be provided to enhance some more meaningful insights.

A model to classify users of social networks based on PageRank

In this paper, we present a model to classify users of Social Networks. In particular, we focus on Social Network Sites. The model is based on the PageRank algorithm. We use the personalization vector to bias the PageRank to some users. We give an explicit expression of the personalization vector that allows the introduction of some typical features of the users of SNSs. We describe the model as a seven-step process. We illustrate the applicability of the model with two examples. One example is based on real links of a Facebook network. We also indicate how to take into account real actions of Facebook users to implement the model.This work is supported by Spanish DGI grant MTM2010-18674.Pedroche Sánchez, F. (2012). A model to classify users of social networks based on PageRank. International Journal of Bifurcation and Chaos. 22(7):1-14. https://doi.org/10.1142/S0218127412501623S114227Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C. (2008). Synchronization in complex networks. Physics Reports, 469(3), 93-153. doi:10.1016/j.physrep.2008.09.002BOCCALETTI, S., LATORA, V., MORENO, Y., CHAVEZ, M., & HWANG, D. (2006). Complex networks: Structure and dynamics. Physics Reports, 424(4-5), 175-308. doi:10.1016/j.physrep.2005.10.009Boldi, P., Santini, M., & Vigna, S. (2009). PageRank. ACM Transactions on Information Systems, 27(4), 1-23. doi:10.1145/1629096.1629097Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-Law Distributions in Empirical Data. SIAM Review, 51(4), 661-703. doi:10.1137/070710111Criado, R., Flores, J., González-Vasco, M. I., & Pello, J. (2007). Choosing a leader on a complex network. Journal of Computational and Applied Mathematics, 204(1), 10-17. doi:10.1016/j.cam.2006.04.024C. De Kerchove and P. Van Dooren, Lectures Notes in Control and Information Sciences 389 (2009) pp. 3–16.Dorogovtsev, S. (2010). Lectures on Complex Networks. doi:10.1093/acprof:oso/9780199548927.001.0001Easley, D., & Kleinberg, J. (2010). Networks, Crowds, and Markets. doi:10.1017/cbo9780511761942Estrada, E., & Higham, D. J. (2010). Network Properties Revealed through Matrix Functions. SIAM Review, 52(4), 696-714. doi:10.1137/090761070Fortunato, S. (2010). Community detection in graphs. Physics Reports, 486(3-5), 75-174. doi:10.1016/j.physrep.2009.11.002Granovetter, M. S. (1973). The Strength of Weak Ties. American Journal of Sociology, 78(6), 1360-1380. doi:10.1086/225469Haveliwala, T. H. (2003). Topic-sensitive pagerank: A context-sensitive ranking algorithm for web search. IEEE Transactions on Knowledge and Data Engineering, 15(4), 784-796. doi:10.1109/tkde.2003.1208999Langville, A. N., & Meyer, C. D. (2006). Google’s PageRank and Beyond. doi:10.1515/9781400830329Lazer, D., Pentland, A., Adamic, L., Aral, S., Barabasi, A.-L., Brewer, D., … Van Alstyne, M. (2009). SOCIAL SCIENCE: Computational Social Science. Science, 323(5915), 721-723. doi:10.1126/science.1167742Lewis, K., Kaufman, J., Gonzalez, M., Wimmer, A., & Christakis, N. (2008). Tastes, ties, and time: A new social network dataset using Facebook.com. Social Networks, 30(4), 330-342. doi:10.1016/j.socnet.2008.07.002Nan Lin, Dayton, P. W., & Greenwald, P. (1978). Analyzing the Instrumental Use of Relations in the Context of Social Structure. Sociological Methods & Research, 7(2), 149-166. doi:10.1177/004912417800700203Mayer, A., & Puller, S. L. (2008). The old boy (and girl) network: Social network formation on university campuses. Journal of Public Economics, 92(1-2), 329-347. doi:10.1016/j.jpubeco.2007.09.001Newman, M. (2010). Networks. doi:10.1093/acprof:oso/9780199206650.001.0001Pedroche Sánchez, F. (2010). Competitivity groups on social network sites. Mathematical and Computer Modelling, 52(7-8), 1052-1057. doi:10.1016/j.mcm.2010.02.031Sabater, J., & Sierra, C. (2005). Review on Computational Trust and Reputation Models. Artificial Intelligence Review, 24(1), 33-60. doi:10.1007/s10462-004-0041-5Serra-Capizzano, S. (2005). Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation. SIAM Journal on Matrix Analysis and Applications, 27(2), 305-312. doi:10.1137/s0895479804441407Vasalou, A., Joinson, A. N., & Courvoisier, D. (2010). Cultural differences, experience with social networks and the nature of «true commitment» in Facebook. International Journal of Human-Computer Studies, 68(10), 719-728. doi:10.1016/j.ijhcs.2010.06.00

On graphs associated to sets of rankings

In this paper we analyze families of rankings by studying structural properties of graphs. Given a finite number of elements and a set of rankings of those elements, two elements compete when they exchange their relative positions in at least two rankings, and we can associate an undirected graph to a set of rankings by connecting elements that compete. We call this graph a competitivity graph. Competitivity graphs have already appeared in the literature as co-comparability graphs, f-graphs or intersection graphs associated to a concatenation of permutation diagrams. We introduce certain important sets of nodes in a competitivity graph. For example, nodes that compete among them form a competitivity set and nodes connected by chains of competitors form a set of eventual competitors. These sets are analyzed and a method to obtain sets of eventual competitors directly from a set of rankings is shown. © 2015 Elsevier B.V.This paper was partially supported by Spanish MICINN Funds and FEDER Funds MTM2009-13848, MTM2010-16153 and MTM2010-18674, and Junta de Andalucia Funds FQM-264. The authors would like to thank an anonymous referee for the valuable comments and remarks.Criado Herrero, R.; García, E.; Pedroche Sánchez, F.; Romance, M. (2016). On graphs associated to sets of rankings. Journal of Computational and Applied Mathematics. 291:497-508. doi:10.1016/j.cam.2015.03.009S49750829

Leadership groups on Social Network Sites based on Personalized PageRank

n this paper we present a new framework to identify leaders in a Social Network Site using the Personalized PageRank vector. The methodology is based on the concept of Leadership group recently introduced by one of the authors. We show how to analyze the structure of the Leadership group as a function of a single parameter. Zachary¿s network and a Facebook university network are used to illustrate the applicability of the model.We thank an unknown referee who made some suggestive comments that improved the readability of the paper. This work is supported by Spanish DGI grant MTM2010-18674.Pedroche Sánchez, F.; Moreno, F.; González, A.; Valencia, A. (2013). Leadership groups on Social Network Sites based on Personalized PageRank. Mathematical and Computer Modelling. 57(7-8):1891-1896. https://doi.org/10.1016/j.mcm.2011.12.026S18911896577-

Brazilian Congress structural balance analysis

In this work, we study the behavior of Brazilian politicians and political parties with the help of clustering algorithms for signed social networks. For this purpose, we extract and analyze a collection of signed networks representing voting sessions of the lower house of Brazilian National Congress. We process all available voting data for the period between 2011 and 2016, by considering voting similarities between members of the Congress to define weighted signed links. The solutions obtained by solving Correlation Clustering (CC) problems are the basis for investigating deputies voting networks as well as questions about loyalty, leadership, coalitions, political crisis, and social phenomena such as mediation and polarization.Comment: 27 pages, 15 tables, 6 figures; entire article was revised, new references added (including international press); correcting typing error