Skip to main content Accessibility help

Opinion-based centrality in multiplex networks: A convex optimization approach



Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when controlling an external influence able to affect each node individually. We find a mathematical closed form of this problem, and use its solution to derive our centrality measure. According to the opinion centrality, the more a node is worth investing external influence, and the more it is central. We perform an empirical study of the proposed centrality over a toy network, as well as a collection of real-world networks. Our measure is generally negatively correlated with existing multiplex centrality measures, and highlights different types of nodes, accordingly to its definition.



Hide All
Battiston, F., Nicosia, V., & Latora, V. (2014). Structural measures for multiplex networks. Physical Review E, 89 (3), 032804.
Bimpikis, K., Ozdaglar, A., & Yildiz, E. (2016). Competitive Targeted Advertising over Networks. Operations Research, 64 (3), 705720.
Boccaletti, S., Bianconi, G., Criado, R., del Genio, C. I., Gómez-Gardeñes, J., Romance, M., . . . Zanin, M. (2014). The structure and dynamics of multilayer networks. Physics Reports, 544 (1), 1122.
Borkar, V. S. (2008). Stochastic approximation – a dynamical systems viewpoint. Cambridge Books.
Borkar, V. S., & Karnik, A. (2011). Controlled gossip. In Proceedings of the, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), IEEE, pp. 707711.
Borkar, V. S., Nair, J., & Sanketh, N. (2010). Manufacturing consent. In Communication, Control, and Computing (allerton), IEEE, pp. 15501555.
Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge University Press.
Breiger, R., Boorman, S., & Arabie, P. (1975). An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling. Journal of Mathematical Psychology, 12 (3), 328383.
Breiger, R., & Pattison, P. (1986). Cumulated social roles: The duality of persons and their algebras. Social Networks, 8 (3), 215256.
Cardillo, A., Gómez-Gardeñes, J., Zanin, M., Romance, M., Papo, D., del Pozo, F., & Boccaletti, S. (2013). Emergence of network features from multiplexity. Scientific Reports, 3, 1344.
Chakraborty, T., & Narayanam, R. (2016). Cross-layer betweenness centrality in multiplex networks with applications. In Proceedings of the 32nd IEEE International Conference on Data Engineering, pp. 397–408.
Coleman, J., Katz, E., & Menzel, H. (1957). The diffusion of an innovation among physicians. Sociometry, 20 (4), 253270.
Coscia, M., Rossetti, G., Pennacchioli, D., Ceccarelli, D., & Giannotti, F. (2013). You know because i know: A multidimensional network approach to human resources problem. In IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, pp. 434–441.
de Domenico, M., Lancichinetti, A., Arenas, A., & Rosvall, M. (2015a). Identifying modular flows on multilayer networks reveals highly overlapping organization in interconnected systems. Physical Review X, 5 (1), 011027.
de Domenico, M., Nicosia, V., Arenas, A., & Latora, V. (2015c). Structural reducibility of multilayer networks. Nature Communications, 6, 6864.
de Domenico, M., Porter, M. A., & Arenas, A. (2015b). Muxviz: A tool for multilayer analysis and visualization of networks. Journal of Complex Networks, 3 (2), 159176.
de Domenico, M., Solé-Ribalta, A., Cozzo, E., Kivelä, M., Moreno, Y., Porter, M. A., . . . Arenas, A. (2013). Mathematical formulation of multilayer networks. Physical Review X, 3 (4), 041022.
de Domenico, M., Solé-Ribalta, A., Gómez, S., & Arenas, A. (2014). Navigability of interconnected networks under random failures. Proceedings of the National Academy of Sciences, 11 (23), 83518356.
DeGroot, M. H. (1974). Reaching a consensus. Journal of the American Statistical Association, 69 (345), 118121.
Halu, A., Mondragón, R. J., Panzarasa, P., & Bianconi, G. (2013). Multiplex pagerank. Plos One, 8 (10), e78293.
Horn, R. A., & Johnson, C. R. (2012). Matrix analysis. New York, NY, USA, Cambridge University Press.
Jackson, M. O. (2008). Social and economic networks. Vol. 3. Princeton: Princeton University Press.
Kapferer, B. (1972). Strategy and transaction in an african factory. Manchester, UK, Manchester University Press.
Kivelä, M., Arenas, A., Barthélemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014). Multilayer networks. Journal of Complex Networks, 2 (3), 203271.
Knoke, D., & Wood, J. (1981). Organized for action: Commitment in voluntary associations. New Brunswick, NJ, USA, Rutgers University Press.
Kolda, T., & Bader, B. W. (2006). The tophits model for higher-order web link analysis. SIAM Data Mining Conference Workshop on Link Analysis, Counterterrorism and Security.
Lazega, E. (2001). The collegial phenomenon: The social mechanisms of cooperation among peers in a corporate law partnership. Oxford, UK, Oxford University Press.
Magnani, M., Micenkova, B., & Rossi, L. (2013). Combinatorial analysis of multiple networks. arxiv, cs.SI, 1303.4986.
Magnani, M., & Rossi, L. (2011). The ml-model for multi-layer social networks. In International Conference on Advances in Social Networks Analysis and Mining, pp. 5–12.
Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic theory. Vol. 1. Oxford, UK, Oxford University Press.
Ng, M. K., Li, X., & Ye, Y. (2011). Multirank: Co-ranking for objects and relations in multi-relational data. In Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1217–1225.
Roethlisberger, F., & Dickson, W. (1939). Management and the worker. Cambridge, UK, Cambridge University Press.
Solá, L., Romance, M., Criado, R., Flores, J., García del Amo, A., & Boccaletti, S. (2013). Eigenvector centrality of nodes in multiplex networks. Chaos, 23 (3), 033131.
Solé-Ribalta, A., de Domenico, M., Gómez, S., & Arenas, A. (2014). Centrality rankings in multiplex networks. In ACM Conference on Web Science, pp. 149–155.
Solé-Ribalta, A., de Domenico, M., Gómez, S., & Arenas, A. (2016). Random walk centrality in interconnected multilayer networks. Physica D, 323–324, 7379.
Thurman, B. (1979). In the office: Networks and coalitions. Social Networks, 2 (1), 4763.


Type Description Title
Supplementary materials

Reiffers-Masson supplementary material
Reiffers-Masson supplementary material

 Unknown (11.9 MB)
11.9 MB


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed