Balanced clusters and diffusion process in signed networks

Document Type : Research Paper


Department of Industrial Engineering, Tarbiat-Modares University


In this paper we study the topology effects on diffusion process in signed networks. Considering a simple threshold model for diffusion process, it is extended to signed networks and some appropriate definitions are proposed. This model is a basic model that could be extended and applied in analyzing dynamics of many real phenomena such as opinion forming or innovation diffusion in social networks. Studying the model declares that highly balanced dense clusters act as obstacles to diffusion process. This fact is verified by numerical simulations and it is declared that balanced dense clusters limit perturbation diffusion and the rest time. In other words the systems with more compatible communities and balanced clusters act more robust against perturbations. Moreover, the final state majority would be the same of more balanced cluster initially. These structural properties could be useful in analyzing and controlling diffusion process in systems.


Alcántara, J. M., & Rey, P. J. (2012). Linking topological structure and dynamics in ecological
networks. The American Naturalist, 180(2), 186-199.
Balankin, A. S., Martínez Cruz, M. Á., & Martínez, A. T. (2011). Effect of initial concentration and
spatial heterogeneity of active agent distribution on opinion dynamics. Physica A: Statistical
Mechanics and its Applications, 390(21), 3876-3887.
Cartwright, D., & Harary, F. (1956). Structural balance: a generalization of Heider's theory.
Psychological review, 63(5), 277.
Delre, S. A., Jager, W., & Janssen, M. A. (2007). Diffusion dynamics in small-world networks with
heterogeneous consumers. Computational and Mathematical Organization Theory, 13(2), 185-202.
Castellano, C., Fortunato, S., & Loreto, V. (2009). Statistical physics of social dynamics. Reviews of
modern physics, 81(2), 591.
Deroı̈an, F. (2002). Formation of social networks and diffusion of innovations. Research policy,
31(5), 835-846.
Easley, D., & Kleinberg, J. (2010). Networks, crowds, and markets: Reasoning about a highly
connected world. Cambridge University Press.
Granovetter, M. S. (1973). The strength of weak ties. American journal of sociology, 1360-1380.
Heider, F. (1946). Attitudes and cognitive organization. The Journal of psychology, 21(1), 107-112.
J.A. Davis, Clustering and structural balance in graphs, Human Relations 20 (1967) 181–187.
Karsai, M., Perra, N., & Vespignani, A. (2014). Time varying networks and the weakness of strong
ties. Scientific reports, 4.
Li-Sheng, Z., Wei-Feng, G., Gang, H., & Yuan-Yuan, M. (2014). Network dynamics and its
relationships to topology and coupling structure in excitable complex networks. Chinese Physics B,
23(10), 108902.
Lyst, J. A. H. O., Kacperski, K., & Schweitzer, F. (2002). Social impact models of opinion dynamics.
Annual reviews of computational physics, 9, 253-273.
Malandrino, F., Kurant, M., Markopoulou, A., Westphal, C., & Kozat, U. C. (2012, March). Proactive
seeding for information cascades in cellular networks. In INFOCOM, 2012 Proceedings IEEE (pp.
1719-1727). IEEE.
Mustafa, N. H., & Pekeč, A. (2001). Majority consensus and the local majority rule. In Automata,
Languages and Programming (pp. 530-542). Springer Berlin Heidelberg.
Nematzadeh, A., Ferrara, E., Flammini, A., & Ahn, Y. Y. (2014). Optimal Network Modularity for
Information Diffusion. Physical review letters, 113(8), 088701.
Peres, R., Muller, E., & Mahajan, V. (2010). Innovation diffusion and new product growth models: A
critical review and research directions. International Journal of Research in Marketing, 27(2), 91-
Rahmandad, H., & Sterman, J. (2008). Heterogeneity and network structure in the dynamics of
diffusion: Comparing agent-based and differential equation models. Management Science, 54(5), 998-
Sontag, E. D. (2007). Monotone and near-monotone biochemical networks. Systems and Synthetic
Biology, 1(2), 59-87.
Srinivasan, A. R., & Chakraborty, S. (2014, June). Effect of network topology on the controllability
of voter model dynamics using biased nodes. In American Control Conference (ACC), 2014 (pp.
2096-2101). IEEE.
Valente, T. W. (1995). Network models of the diffusion of innovations (Vol. 2, No. 2). Cresskill, NJ:
Hampton Press.
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’networks. nature,
393(6684), 440-442.
Zhou, H., & Lipowsky, R. (2007). Activity patterns on random scale-free networks: Global dynamics
arising from local majority rules. Journal of Statistical Mechanics: Theory and Experiment, 2007(01),