Aashi Shrinate

Aashi Shrinate, Twinkle Tripathy

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.

Aashi Shrinate, Twinkle Tripathy, Laxmidhar Behera

The Friedkin-Johnsen (FJ) model is a popular opinion dynamics model that explains the disagreement that can occur even among closely interacting individuals. Cluster consensus is a special type of disagreement, where agents in a network split into subgroups such that those within a subgroup agree and those in different subgroups disagree. In large-scale social networks, users often distribute into echo chambers (i.e. groups of users with aligned views) while discussing contested issues such as electoral politics, social norms, etc. Additionally, they are exposed only to opinions and news sources that align with their existing beliefs. Hence, the interaction network plays a key role in the formation of an echo chamber. Since cluster consensus can represent echo chambers in a social network, we examine the conditions for cluster consensus under the FJ model with the objective of determining the properties of the interaction network that lead to echo chamber formation. We present topology-based necessary and sufficient conditions for cluster consensus under the FJ model, regardless of the edge weights in the network and stubbornness values (which are difficult to estimate parameters in a social network). A major advantage of the proposed results is that they are applicable to arbitrary digraphs. Moreover, using the proposed conditions, we explain the emergence of bow-tie structures which are often observed in real-world echo chambers. Finally, we also develop a computationally feasible methodology to verify the proposed conditions for cluster consensus.