Opinion Clustering under the Friedkin-Johnsen Model: Agreement in Disagreement
This work addresses a gap in social network analysis by providing topological conditions for opinion clustering, which is incremental as it builds on the well-studied Friedkin-Johnsen framework.
The paper tackles the problem of understanding how opinion clusters form in networks under the Friedkin-Johnsen model by introducing Locally Topologically Persuasive (LTP) agents, and it shows that these agents can be used to design networks to achieve any desired clustering, as demonstrated through simulations.
The convergence of opinions in the Friedkin-Johnsen (FJ) framework is well studied, but the topological conditions leading to opinion clustering remain less explored. To bridge this gap, we examine the role of topology in the emergence of opinion clusters within the network. The key contribution of the paper lies in the introduction of the notion of topologically prominent agents, referred to as Locally Topologically Persuasive (LTP) agents. Interestingly, each LTP agent is associated with a unique set of (non-influential) agents in its vicinity. Using them, we present conditions to obtain opinion clusters in the FJ framework in any arbitrarily connected digraph. A key advantage of the proposed result is that the resulting opinion clusters are independent of the edge weights and the stubbornness of the agents. Finally, we demonstrate using simulation results that, by suitably placing LTP agents, one can design networks that achieve any desired opinion clustering.