Publications and Research

Document Type


Publication Date



We present a study of the dynamic interactions between actors located on complex networks with scale-free and hierarchical scale-free topologies with assortative mixing, that is, correlations between the degree distributions of the actors. The actor’s state evolves according to a model that considers its previous state, the inertia to change, and the influence of its neighborhood. We show that the time evolution of the system depends on the percentage of cooperative or competitive
interactions. For scale-free networks, we find that the dispersion between actors is higher when all interactions are either cooperative or competitive, while a balanced presence of interactions leads to a lower separation. Moreover, positive assortative mixing leads to greater divergence between the states, while negative assortative mixing reduces this dispersion. We also find that hierarchical scale-free networks have both similarities and differences when compared with scale-free networks. Hierarchical scale-free networks, like scale-free networks, show the least divergence for an equal mix of cooperative and competitive interactions between actors. On the other hand, hierarchical scale-free networks, unlike scale-free networks, show much greater divergence when dominated by cooperative rather than competitive actors, and while the formation of a rich club (adding links between hubs) with cooperative interactions leads to greater divergence, the divergence is much less when they are fully competitive. Our findings highlight the importance of the topology where the interaction dynamics take place, and the fact that a balanced presence of cooperators and competitors makes the system more cohesive, compared to the case where one strategy dominates.


Originally published as: Jacobo-Villegas, Eduardo, Bibiana Obregón-Quintana, Lev Guzmán-Vargas, and Larry S. Liebovitch. "Conflict Dynamics in Scale-Free Networks with Degree Correlations and Hierarchical Structure." Entropy, vol. 24, 2022, article 1571.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.