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Consensus protocols play an important role in the study of distributed algorithms. In this paper, we study the effect of bias on two popular consensus protocols, namely, the {\em voter rule} and the {\em 2-choices rule} with binary…
Collective leadership and herding may arise in standard models of opinion dynamics as an interplay of a strong separation of time scales within the population and its hierarchical organization. Using the voter model as a simple opinion…
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…
When modelling epidemics or spread of information on online social networks, it is crucial to include not just the density of the connections through which infections can be transmitted, but also the variability of susceptibility. Different…
We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it…
Opinion dynamics models describe the evolution of behavioral changes within social networks and are essential for informing strategies aimed at fostering positive collective changes, such as climate action initiatives. When applied to…
Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its…
We examine some agreement-dynamics models that are placed on directed random graphs. In such systems a fraction of sites $\exp(-z)$, where $z$ is the average degree, becomes permanently fixed or flickering. In the Voter model, which has no…
We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for…
Several algorithms in prior literature have been proposed which guarantee consensus of normally behaving agents in a network that may contain adversarially behaving agents. These algorithms guarantee that the consensus value lies within the…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…
We study an opinion dynamics model that explores the competition between persuasion and compromise in a population of agents with nearest-neighbor interactions on a two-dimensional square lattice. Each agent can hold either a positive or a…
The outcomes of democratic elections rest on individuals' decision-making that is driven by their varying preferences and beliefs. Individuals may prefer consensus to gridlock, or gridlock to consensus, and information may be fractured via…
Opinion dynamics is of paramount importance as it provides insights into the complex dynamics of opinion propagation and social relationship adjustment. It is assumed in most of the previous works that social relationships evolve much…
We study the ordering dynamics of nonlinear voter models with multiple states, also providing a discussion of the two-state model. The rate with which an individual adopts an opinion scales as the $q$-th power of the number of the…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of…
Opinion formation and disease spreading are among the most studied dynamical processes on complex networks. In real societies, it is expected that these two processes depend on and affect each other. However, little is known about the…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…