Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-22T22:00:21.430Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  06 June 2017

Laboratoire Informatique d'Avignon (LIA)EA 4128, Avignon, France (e-mails:,
Laboratoire Informatique d'Avignon (LIA)EA 4128, Avignon, France (e-mails:,


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.

Research Article
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Battiston, F., Nicosia, V., & Latora, V. (2014). Structural measures for multiplex networks. Physical Review E, 89 (3), 032804.CrossRefGoogle ScholarPubMed
Bimpikis, K., Ozdaglar, A., & Yildiz, E. (2016). Competitive Targeted Advertising over Networks. Operations Research, 64 (3), 705720.Google Scholar
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.Google Scholar
Borkar, V. S. (2008). Stochastic approximation – a dynamical systems viewpoint. Cambridge Books.Google Scholar
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.Google Scholar
Borkar, V. S., Nair, J., & Sanketh, N. (2010). Manufacturing consent. In Communication, Control, and Computing (allerton), IEEE, pp. 15501555.Google Scholar
Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge University Press.Google Scholar
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.Google Scholar
Breiger, R., & Pattison, P. (1986). Cumulated social roles: The duality of persons and their algebras. Social Networks, 8 (3), 215256.CrossRefGoogle Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
Coleman, J., Katz, E., & Menzel, H. (1957). The diffusion of an innovation among physicians. Sociometry, 20 (4), 253270.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
de Domenico, M., Nicosia, V., Arenas, A., & Latora, V. (2015c). Structural reducibility of multilayer networks. Nature Communications, 6, 6864.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
DeGroot, M. H. (1974). Reaching a consensus. Journal of the American Statistical Association, 69 (345), 118121.Google Scholar
Halu, A., Mondragón, R. J., Panzarasa, P., & Bianconi, G. (2013). Multiplex pagerank. Plos One, 8 (10), e78293.Google Scholar
Horn, R. A., & Johnson, C. R. (2012). Matrix analysis. New York, NY, USA, Cambridge University Press.Google Scholar
Jackson, M. O. (2008). Social and economic networks. Vol. 3. Princeton: Princeton University Press.Google Scholar
Kapferer, B. (1972). Strategy and transaction in an african factory. Manchester, UK, Manchester University Press.Google Scholar
Kivelä, M., Arenas, A., Barthélemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014). Multilayer networks. Journal of Complex Networks, 2 (3), 203271.Google Scholar
Knoke, D., & Wood, J. (1981). Organized for action: Commitment in voluntary associations. New Brunswick, NJ, USA, Rutgers University Press.CrossRefGoogle Scholar
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.Google Scholar
Lazega, E. (2001). The collegial phenomenon: The social mechanisms of cooperation among peers in a corporate law partnership. Oxford, UK, Oxford University Press.CrossRefGoogle Scholar
Magnani, M., Micenkova, B., & Rossi, L. (2013). Combinatorial analysis of multiple networks. arxiv, cs.SI, 1303.4986.Google Scholar
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.Google Scholar
Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic theory. Vol. 1. Oxford, UK, Oxford University Press.Google Scholar
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.Google Scholar
Roethlisberger, F., & Dickson, W. (1939). Management and the worker. Cambridge, UK, Cambridge University Press.Google Scholar
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.Google Scholar
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.Google Scholar
Solé-Ribalta, A., de Domenico, M., Gómez, S., & Arenas, A. (2016). Random walk centrality in interconnected multilayer networks. Physica D, 323–324, 7379.Google Scholar
Thurman, B. (1979). In the office: Networks and coalitions. Social Networks, 2 (1), 4763.Google Scholar
Supplementary material: File

Reiffers-Masson supplementary material

Reiffers-Masson supplementary material

Download Reiffers-Masson supplementary material(File)
File 11.9 MB