Skip to main content Accessibility help
×
×
Home

Vulnerability and power on networks

  • ENRICO BOZZO (a1), MASSIMO FRANCESCHET (a1) and FRANCA RINALDI (a1)

Abstract

Inspired by socio-political scenarios, like dictatorships, in which a minority of people exercise control over a majority of weakly interconnected individuals, we propose vulnerability and power measures defined on groups of actors of networks. We establish an unexpected connection between network vulnerability and graph regularizability. We use the Shapley value of coalition games to introduce fresh notions of vulnerability and power at node level defined in terms of the corresponding measures at group level. We investigate the computational complexity of computing the defined measures, both at group and node levels, and provide effective methods to quantify them. Finally we test vulnerability and power on both artificial and real networks.

Copyright

References

Hide All
Berge, C. (1978). Regularizable graphs I. Discrete Mathematics, 23, 8589.
Berge, C. (1981). Some common properties for regularizable graphs, edge-critical graphs and B-graphs. In Saito, N., & Nishizeki, T. (Eds.), Graph theory and algorithms. Lecture Notes in Computer Science, vol. 108 (pp. 108123). Berlin: Springer.
Berkman, L. F., & Glass, T. (2000). Social integration, social networks, social support, and health. In Berkman, L. F., & Kawachi, I. (Eds.), Social epidemiology. New York: Oxford University Press.
Bonacich, P. (1987). Power and centrality: A family of measures. American Journal of Sociology, 92 (5), 11701182.
Burt, R. S. (2004). Structural holes and good ideas. American Journal of Sociology, 110 (2), 349399.
Cobb, N. K., Graham, A. L., & Abrams, D. B. (2010). Social network structure of a large online community for smoking cessation. American Journal Public Health, 100 (7), 12821289.
Everett, M. G., & Borgatti, S. P. (1999). The centrality of groups and classes. Journal of Mathematical Sociology, 23 (3), 181201.
Franceschet, M. (2011). PageRank: Standing on the shoulders of giants. Communications of the ACM, 54 (6), 92101.
Godsil, C., & Royle, G. F. (2001). Algebraic graph theory. New York: Springer.
Grofman, B., & Owen, G. (1982). A game-theoretic approach to measuring centrality in social networks. Social Networks, 4, 213224.
Grötschel, M., Lovász, L., & Schrijver, A. (1988). Geometric algorithms and combinatorial optimization. Heidelberg: Springer.
Hayes, B. (2006). Connecting the dots. American Scientist, 94 (5), 400404.
Heaney, C. A., & Israel, B. A. (2008). Social networks and social support. In Glanz, K., Rimer, B. K., & Viswanath, K. (Eds.), Health behavior and health education: Theory, research and practice. San Francisco: Jossey-Bass.
Hoory, S., Linial, N., & Wigderson, A. (2006). Expander graphs and their applications. Bulletin of the American Mathematical Society, 43, 439561.
Iwata, S. (2008). Submodular function minimization. Mathematical Programming, 112, 4564.
Kets, W., Iyengar, G., Sethi, R., & Bowles, S. (2011). Inequality and network structure. Games and Economic Behavior, 73 (1), 215226.
Khachiyan, L. (1980). Polynomial algorithms for linear programming. Ussr Computational Mathematics and Mathematical Physics, 20, 5168.
Lovász, L., & Plummer, M. D. (1986). Matching theory. Annals of discrete mathematics, vol. 29. Amsterdam: North Holland.
Michalak, T. P., Aadithya, K. V., Szczepański, P. L., Ravindran, B., & Jennings, N. R. (2013). Efficient computation of the Shapley value for game-theoretic network centrality. Journal of Artificial Intelligence Research, 46, 607650.
Newman, M. E. J. (2010). Networks: An introduction. Oxford: Oxford University Press.
Newman, M. E. J., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69, 026113.
Osborne, M. J., & Rubinstein, A. (1994). A course in game theory. Annals of discrete mathematics. Cambridge, MA: MIT Press.
Pulleyblank, W. R. (1979). Minimum node covers and 2-bicritical graphs. Mathematical Programming, 17, 91103.
Schrijver, A. (2003). Combinatorial optimization - polyhedra and efficiency. Berlin: Springer.
Shapley, L. S. (1971). Cores of convex games. International Journal of Game Theory, 1 (1), 1126.
Suri, N., & Narahari, Y. (2010). A Shapley value-based approach to discover influential nodes in social networks. IEEE Transactions on Automation Science and Engineering, 99, 118.
Szczepański, P. L., Michalak, T., & Rahwan, T. (2012). A new approach to betweenness centrality based on the Shapley value. Joint Conference on Autonomous Agents and Multi-Agent Systems, pp. 239–246.
Tutte, W. T. (1953). The 1-factors of oriented graphs. Proceedings of the American Mathematical Society, 4, 922931.
van den Brink, R., & Gilles, R. P. (1994). A social power index for hierarchically structured populations of economic agents. In Gilles, R. P., & Ruys, P. H. M. (Eds.), Imperfections and behavior in economic organizations. Theory and Decision Library, vol. 11 (pp. 279318). Netherlands: Springer.
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393, 440442.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Network Science
  • ISSN: 2050-1242
  • EISSN: 2050-1250
  • URL: /core/journals/network-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

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