  In this work, we investigate the evolution of polarization, influence, and
domination in online interaction networks. Twitter data collected before and
during the 2022 Brazilian elections is used as a case study. From a theoretical
perspective, we develop a methodology called d-modularity that allows
discovering the contribution of specific groups to network polarization using
the well-known modularity measure. While the overall network modularity
(somewhat unexpectedly) decreased, the proposed group-oriented approach allows
concluding that the contribution of the right-leaning community to this
modularity increased, remaining very high during the analyzed period. Our
methodology is general enough to be used in any situation when the contribution
of specific groups to overall network modularity and polarization is needed to
investigate. Moreover, using the concept of partial domination, we are able to
compare the reach of sets of influential profiles from different groups and
their ability to accomplish coordinated communication inside their groups and
across segments of the entire network during some specific time window. We show
that in the whole network, the left-leaning high-influential information
spreaders dominated, reaching a substantial fraction of users with fewer
spreaders. However, when comparing domination inside the groups, the results
are inverse. Right-leaning spreaders dominate their communities using few
nodes, showing as the most capable of accomplishing coordinated communication.
The results bring evidence of extreme isolation and the ease of accomplishing
coordinated communication that characterized right-leaning communities during
the 2022 Brazilian elections.
