  Agent-based models of opinion dynamics allow one to examine the spread of
opinions between entities and to study phenomena such as consensus,
polarization, and fragmentation. By studying a model of opinion dynamics on a
social network, one can explore the effects of network structure on these
phenomena. In social networks, some individuals share their ideas and opinions
more frequently than others. These disparities can arise from heterogeneous
sociabilities, heterogeneous activity levels, different prevalences to share
opinions when engaging in a social-media platform, or something else. To
examine the impact of such heterogeneities on opinion dynamics, we generalize
the Deffuant--Weisbuch (DW) bounded-confidence model (BCM) of opinion dynamics
by incorporating node weights. The node weights allow us to model agents with
different probabilities of interacting. Using numerical simulations, we
systematically investigate (using a variety of network structures and
node-weight distributions) the effects of node weights, which we assign
uniformly at random to the nodes. We demonstrate that introducing heterogeneous
node weights results in longer convergence times and more opinion fragmentation
than in a baseline DW model. The node weights in our BCM allow one to consider
a variety of sociological scenarios in which agents have heterogeneous
probabilities of interacting with other agents.
