arXiv subjects

Aashi Shrinate

Publications and source records attributed to Aashi Shrinate.

9 recordsLinked to original sources

arXiv2026

Influence Enhancement in Opinion Dynamics Using Edge Modification: A Kron Reduction-Based Approach

With the emergence of online social networks as a primary platform for advertising and advocacy, enhancing a user's influence has become of significant interest. In this paper, we investigate this problem under the Friedkin Johnsen opinion dynamics model, wherein stubborn agents influence the opinions of other agents in the network. Unlike most of the existing works, we leverage topological properties of the network to increase the influence of a desired stubborn agent. Specifically, we introduce the notion of edge modification, which mimics the mechanism of recommendations in social networks. First, we present a topology-based condition that identifies edge modifications that always increase the influence of a desired stubborn agent. It is shown that the impact of the chosen edge modifications remains robust to changes in parameters such as stubbornness and the interaction weights. Thereafter, we formulate a discrete optimisation problem to identify a set of edge modifications that maximise the agent's influence centrality. We present a computationally efficient approximate solution to the optimisation problem. Finally, we demonstrate the effectiveness of our approach on the Friedkin-Johnsen opinion dynamics over the Erdos Renyi random graph.

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arXiv2026

Opinion Clustering under the Friedkin-Johnsen Model: Agreement in Disagreement

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.

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arXiv2026

Topological Conditions for Echo Chamber Formation under the FJ model: A Cluster Consensus-based Approach

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.

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arXiv2025

Topology-based Conditions for Multiconsensus under the Signed Friedkin-Johnsen Model

In this paper, we address the multiconsensus problem in networked systems, where agents are partitioned into disjoint subgroups and the states of agents within a subgroup are driven to consensus. Our objective is to present a distributed control law that leads to multiconsensus in signed digraphs. To this end, we examine the convergence of opinions under the opposing rule-based signed Friedkin-Johnsen (SFJ) model and present conditions that lead to multiconsensus under this model. Interestingly, the proposed conditions depend only on graph topology and signed interactions and not on the edge weights of the network. Consequently, the proposed SFJ-based control law relaxes the in-degree balance and homogeneity of trust-distrust, frequently assumed in the literature. Finally, we add simulation results to demonstrate the proposed conditions for multiconsensus.

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arXiv2025

A Signed Friedkin-Johnsen Model for Arbitrary Network Topologies

The paper presents an opposing rule-based signed Friedkin-Johnsen (SFJ) model for the evolution of opinions in arbitrary network topologies with signed interactions and stubborn agents. The primary objective of the paper is to analyse the emergent behaviours of the agents under the proposed rule and to identify the key agents which contribute to the final opinions, characterised as influential agents. We start by presenting some convergence results which show how the opinions of the agents evolve for a signed network with any arbitrary topology. Throughout the paper, we classify the agents as opinion leaders (sinks in the associated condensation graph) and followers (the rest). In general, it has been shown in the literature that opinion leaders and stubborn agents drive the opinions of the group. However, the addition of signed interactions reveals interesting behaviours wherein opinion leaders can now become non-influential or less influential. Further, while the stubborn agents always continue to remain influential, they might become less influential owing to signed interactions. Additionally, the signed interactions can drive the opinions of the agents outside of the convex hull of their initial opinions. Thereafter, we propose the absolute influence centrality measure, which allows us to quantify the overall influence of all the agents in the network and also identify the most influential agents. Unlike most of the existing measures, it is applicable to any network topology and considers the effect of both stubbornness and signed interactions. Finally, simulations are presented for the Bitcoin Alpha dataset to elaborate the proposed results.

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arXiv2025

Leveraging Network Topology in a Two-way Competition for Influence in the Friedkin-Johnsen Model

In this paper, we consider two stubborn agents who compete for `influence' over a strongly connected group of agents. This framework represents real-world contests, such as competition among firms, two-party elections, and sports rivalries, among others. Considering stubbornness of agents to be an immutable property, we utilise the network topology alone to increase the influence of a preferred stubborn agent. We demonstrate this on a special class of strongly connected networks by identifying the supporters of each of the stubborn agents in such networks. Thereafter, we present sufficient conditions under which a network perturbation always increases the influence of the preferred stubborn agent. A key advantage of the proposed topology-based conditions is that they hold independent of the edge weights in the network. Most importantly, we assert that there exists a sequence of perturbations that can make the lesser influential stubborn agent more influential. Finally, we demonstrate our results over the Sampson's Monastery dataset.

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arXiv2024

Towards influence centrality: where to not add an edge in the network?

In this work, we consider a strongly connected group of individuals involved in decision-making. The opinions of the individuals evolve using the Friedkin-Johnsen (FJ) model. We consider that there are two competing `influencers' (stubborn agents) vying for control over the final opinion of the group. We investigate the impact of modifying the network interactions on their respective control over the final opinions (influence centrality). We use signal flow graphs (SFG) to relate the network interactions with the influence that each `influencer' exerts on others. We present the sufficient conditions on the edge modifications which lead to the increase of the influence of an `influencer' at the expense of the other. Interestingly, the analysis also reveals the existence of redundant edge modifications that result in no change in the influence centrality of the network. We present several numerical examples to illustrate these results.

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arXiv2024

External Bias and Opinion Clustering in Cooperative Networks

In this work, we consider a group of n agents which interact with each other in a cooperative framework. A Laplacian-based model is proposed to govern the evolution of opinions in the group when the agents are subjected to external biases like agents' traits, news, etc. The objective of the paper is to design a control input which leads to any desired opinion clustering even in the presence of external bias factors. Further, we also determine the conditions which ensure the reachability to any arbitrary opinion states. Note that all of these results hold for any kind of graph structure. Finally, some numerical simulations are discussed to validate these results.

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arXiv2024

Absolute centrality in a signed Friedkin-Johnsen based model: a graphical characterisation of influence

This paper studies the evolution of opinions governed by a Friedkin Johnsen (FJ) based model in arbitrary network structures with signed interactions. The agents contributing to the opinion formation are characterised as being influential. Initially, the agents are classified as opinion leaders and followers based on network connectivity and the nature of interactions. However, the addition of stubbornness leads to interesting behaviours wherein a non influential agent can now become influential and vice versa. Thereafter, a signal flow graph (SFG) based method is proposed to quantify the influence of an influential agents' opinions. Additionally, it helps illustrate the role played by network topology in shaping the final opinions of the agents. Based on this analysis, the absolute centrality measure is proposed to determine the overall influence of all the agents in the network. Unlike most of the existing measures, it is applicable to any network structure and considers the effect of stubbornness and antagonism. Examples are presented throughout the paper to illustrate and validate these results.

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