Understanding and quantifying polarization in social systems is important because of many reasons. It could for instance help to avoid segregation and conflicts in the society or to control polarized debates and predict their outcomes. In this paper, we present a version of the q-voter model of opinion dynamics with two types of responses to social influence: conformity (like in the original q-voter model) and anticonformity. We put the model on a social network with the double-clique topology in order to check how the interplay between those responses impacts the opinion dynamics in a population divided into two antagonistic segments. The model is analyzed analytically, numerically and by means of Monte Carlo simulations. Our results show that the system undergoes two bifurcations as the number of cross-links between cliques changes. Below the first critical point, consensus in the entire system is possible. Thus, two antagonistic cliques may share the same opinion only if they are loosely connected. Above that point, the system ends up in a polarized state.

We describe collaboration networks consisting of research projects funded by the European Union (EU) and the organizations involved in those projects. The networks are substantial in terms of size, complexity, and potential impact on research policies and national economies in the EU. In empirical determinations of the network properties, we observe characteristics similar to those of other collaboration networks, including scale-free degree distributions, small diameter, and high clustering. We present some plausible models for the formation and structure of networks with the observed properties.