arXiv subjects

Twinkle Tripathy

Publications and source records attributed to Twinkle Tripathy.

At least 19 recordsLinked to original sources

arXiv2026

Structural Sign Herdability in Temporal Networks: A Sufficient Condition via $\pi_p$-Graphs

In this letter, we study the herdability of temporally switching directed networks. A temporal network is modeled as a switched system with a fixed switching sequence, which imposes more restrictive herdability conditions than those of conventional switched systems. By exploiting the relationship between temporal walks and the entries of the controllability matrix, we derive sufficient conditions for herdability. We further show that the magnitude of edge weights influences the sign pattern of the controllability matrix, thereby affecting herdability. Consequently, herdability in temporal networks depends not only on the network topology and switching durations, but also on the magnitude of the edge weights. Motivated by this observation, we establish equivalent graph-theoretic conditions for structural sign ($\mathcal{SS}$) herdability in temporal networks. In particular, we introduce the union multigraph of temporal subsystems and propose the notion of a $\pi$-graph. We show that the existence of a $\pi_p$-graph, which is a temporally evolving $\pi$-graph, is sufficient to guarantee $\mathcal{SS}$ herdability. Illustrative examples are provided to demonstrate the proposed results.

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arXiv2026

Bearing-based Circumnavigation with Collision Avoidance in Time-varying Graphs under Limited Target Information

In this paper, we study distributed circumnavigation of a stationary target by a heterogeneous team of agents. Each agent is modelled as a disk rather than a point mass to account for its physical dimensions. The target location is assumed to be accessible only to a small subset of agents, called leaders. The rest, called followers, therefore use only local information available from their designated out-neighbour in the interaction graph characterised by the selection of nearest neighbours. By controlling only angular speeds, we develop a distributed guidance law to circumnavigate a stationary target. The proposed guidance law works for both static and time-varying interaction graphs. Inter-agent collision avoidance is enforced through a logarithmic Barrier Lyapunov (BLF) Function, which guarantees forward invariance of the collision-free set. We show that every follower converges to circumnavigation about the same target as the leader at the end of its directed path in the interaction graph, provided the initial conditions are admissible. Numerical simulations illustrate the effectiveness of the proposed method for both static and time-varying topologies.

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arXiv2026

Bearing Only Distributed Circumnavigation with Limited Target Information for Asymmetric Dubins Vehicles

In this paper, we present a class of bearing based distributive nonlinear guidance laws for the cooperative circumnavigation of a stationary target by a heterogeneous team of asymmetric Dubins vehicles. In such a vehicle, the maximal left and right turn capabilities are non uniform. In the given framework, the location of the target is known only to a small subset of the vehicles, called the leaders. The uninformed vehicles, called the followers, use information from their out neighbours in the communication graph, constructed using the nearest neighbour rule. A class of guidance laws is formulated that relies solely on the heading angle and line of sight angles of a designated out neighbour of the vehicle in the graph. Using Zubov theorem, we prove that the proposed guidance laws achieve global asymptotic stability under angular speed only control and ensure the convergence of the trajectories of all the Dubins vehicles to a common centre. The proposed results are validated through numerical simulations.

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arXiv2026

Structural Sign Herdability in Temporally Switching Networks with Fixed Topology

This paper investigates structural herdability in a special class of temporally switching networks with fixed topology. We show that when the underlying digraph remains unchanged across all snapshots, the network attains complete SS herdability even in the presence of signed or layer dilations, a condition not applicable to static networks. This reveals a fundamental structural advantage of temporal dynamics and highlights a novel mechanism through which switching can overcome classical obstructions to herdability. To validate these conclusions, we utilize a more relaxed form of sign matching within each snapshot of the temporal network. Furthermore, we show that when all snapshots share the same underlying topology, the temporally switching network achieves $\mathcal{SS}$ herdability within just two snapshots, which is fewer than the number required for structural controllability. Several examples are included to demonstrate these results.

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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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arXiv2026

Distributed Circumnavigation Using Bearing Based Control with Limited Target Information

In this paper, we address the problem of circumnavigation of a stationary target by a heterogeneous group comprising of $\textbf{n}$ autonomous agents, having unicycle kinematics. The agents are assumed to have constant linear speeds, we control only the angular speeds. Assuming limited sensing capabilities of the agents, only a subset of agents, termed as \textit{leaders}, know the target location. The rest, termed as \textit{followers}, do not. We propose a distributed guidance law which drives all the agents towards the desired objective; global asymptotic stability (GAS) is ensured by using Zubov's theorem. The efficacy of the approach is demonstrated through both numerical simulations and hardware experiments.

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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

Steering Opinion Dynamics in Signed Time-Varying Networks via External Control Input

This paper studies targeted opinion formation in multi-agent systems evolving over signed, time-varying directed graphs. The dynamics of each agent's state follow a Laplacian-based update rule driven by both cooperative and antagonistic interactions in the presence of exogenous factors. We formulate these exogenous factors as external control inputs and establish a suitable controller design methodology enabling collective opinion to converge to any desired steady-state configuration, superseding the natural emergent clustering or polarization behavior imposed by persistently structurally balanced influential root nodes. Our approach leverages upper Dini derivative analysis and Grönwall-type inequalities to establish exponential convergence for opinion magnitude towards the desired steady state configuration on networks with uniform quasi-strong $δ$-connectivity. Finally, the theoretical results are validated through extensive numerical simulations.

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arXiv2025

Structural sign herdability of linear time-invariant systems:theory and design for arbitrary network structures

The objective of this paper is to investigate graph-theoretic conditions for structural herdability of an LTI system. In particular, we are interested in the structural sign (SS) herdability of a system wherein the underlying digraph representing it is signed. Structural herdability finds applications in various domains like power networks, biological networks, opinion dynamics, multi-robot shepherding, etc. We begin the analysis by introducing a layered graph representation Gs of the signed digraph G; such a representation allows us to capture the signed distances between the nodes with ease. We construct a subgraph of G_s that characterizes paths of identical signs between layers and uniform path lengths, referred to as a layer-wise unisigned graph LUG(G_s). A special subgraph of an LUG(G_s), denoted as an LUG^H(G_s), is key to achieving SS herdability. This is because we prove that an LTI system is SS herdable if and only if there exists an LUG^H(G_s) which covers all the nodes of the given digraph. To the best of our knowledge, such a graphical test is one of the first methods which allows us to check SS herdability for arbitrary digraph topologies. Interestingly, the analysis also reveals that a system can be SS herdable even in the presence of (signed and layer) dilation in the associated digraph (note that such a behaviour has been shown to be impossible in directed trees). Additionally, we also extend these results to digraphs with multiple leader and driver nodes. In order to illustrate all the results, we present numerous examples throughout the paper.

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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

Laplacian Flows in Complex-valued Directed Networks: Analysis, Design, and Consensus

In the interdisciplinary field of network science, a complex-valued network, with edges assigned complex weights, provides a more nuanced representation of relationships by capturing both the magnitude and phase of interactions. Additionally, an important application of this setting arises in distribution power grids. Motivated by the richer framework, we study the necessary and sufficient conditions for achieving consensus in both strongly and weakly connected digraphs. The paper establishes that complex-valued Laplacian flows converge to consensus subject to an additional constraint termed as real dominance which relies on the phase angles of the edge weights. Our approach builds on the complex Perron-Frobenius properties to study the spectral properties of the Laplacian and its relation to graphical conditions. Finally, we propose modified flows that guarantee consensus even if the original network does not converge to consensus. Additionally, we explore diffusion in complex-valued networks as a dual process of consensus and simulate our results on synthetic and real-world networks.

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arXiv2025

Finite time max-consensus for simultaneous target interception in switching graph topologies

In this paper, we propose a distributed guidance law for the simultaneous interception of a stationary target. For a group of `n' heterogeneous pursuers, the proposed guidance law establishes the necessary conditions on static graphs that ensure simultaneous target interception, regardless of the initial conditions of the pursuers. Building on these results, we also establish the necessary conditions for achieving simultaneous interception in switching graph topologies as well. The major highlight of the work is that the target interception occurs in finite time for both static and switching graph topologies. We demonstrate all of these results through numerical simulations.

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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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arXiv2025

Dominant Groups and Asymmetric Polarization in Generalized Quasi-Structurally Balanced Networks

The paper focuses on the phenomenon of asymmetric polarization arising in the presence of a dominant group in the network. The existing works in the literature analyze polarization primarily in structurally and quasi-structurally balanced networks. In this work, we introduce generalized quasi-structurally balanced (GQSB) networks, which include both of these networks as special cases. In the presence of a dominant group, a GQSB network has a unique bipartition: the dominant group (and its allies) and the remaining agents. The dominant group's superior influence results in an asymmetry in how the inter-subset antagonistic interactions are perceived by both of the subsets. This, in turn, leads to asymmetry in the final polarized opinions. To model this behavior, we propose a generalized Laplacian flow for undirected GQSB networks with a dominant group and establish necessary and sufficient conditions for achieving asymmetric polarization. The theoretical results presented in this paper are validated through numerical simulations on the Highland Tribes real-world 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

Are the flows of complex-valued Laplacians and their pseudoinverses related?

Laplacian flows model the rate of change of each node's state as being proportional to the difference between its value and that of its neighbors. Typically, these flows capture diffusion or synchronization dynamics and are well-studied. Expanding on these classical flows, we introduce a pseudoinverse Laplacian flow system, substituting the Laplacian with its pseudoinverse within complex-valued networks. Interestingly, for undirected graphs and unsigned weight-balanced digraphs, Laplacian and the pseudoinverse Laplacian flows exhibit an interdependence in terms of consensus. To show this relation, we first present the conditions for achieving consensus in the pseudoinverse Laplacian flow system using the property of real eventually exponentially positivity. Thereafter, we show that the pseudoinverse Laplacian flow system converges to consensus if and only if the Laplacian flow system achieves consensus in the above-mentioned networks. However, these are only the sufficient conditions for digraphs. Further, we illustrate the efficacy of the proposed approach through examples, focusing primarily on power networks.

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