With the emergence of Online Social Networks (OSNs) as a major platform of communication, its abuse to spread misinformation has become a major threat to our society. In this paper, we study the misinformation containment problem in OSN. Given a snapshot of the OSN with a set of misinformed nodes, and a budget in terms of maximum number of seed nodes, the problem is to select the seed nodes, referred here as the beacon nodes, to plant the correct information, to minimize and eventually eradicate the misinformation at the earliest. We leverage the community structure of the OSN to select the beacon nodes, prioritizing the Community Boundary Nodes. To the best of our knowledge, this is the first work to exploit the topology of the OSN to combat misinformation spread. A modified form of Independent Cascade Model is followed to study the adversarial propagation of both misinformation and the correct information. Simulation on real data set shows that the proposed algorithm outperforms earlier algorithm [1] significantly in terms of maximum (average) infected time and the point of decline.

With the development of social networks, the impact of rumor propagation on human lives is more and more significant. Due to the change of propagation mode, traditional rumor propagation models designed for word-of-mouth process may not be suitable for describing the rumor spreading on social networks. To overcome this shortcoming, we carefully analyze the mechanisms of rumor propagation and the topological properties of large-scale social networks, then propose a novel model based on the physical theory. In this model, heat energy calculation formula and Metropolis rule are introduced to formalize this problem and the amount of heat energy is used to measure a rumor’s impact on a network. Finally, we conduct track experiments to show the evolution of rumor propagation, make comparison experiments to contrast the proposed model with the traditional models, and perform simulation experiments to study the dynamics of rumor spreading. The experiments show that (1) the rumor propagation simulated by our model goes through three stages: rapid growth, fluctuant persistence and slow decline; (2) individuals could spread a rumor repeatedly, which leads to the rumor’s resurgence; (3) rumor propagation is greatly influenced by a rumor’s attraction, the initial rumormonger and the sending probability.

With the advent of online networks, societies have become substantially more interconnected with individual members able to easily both maintain and modify their own social links. Here, we show that active network maintenance exposes agents to confirmation bias, the tendency to confirm one's beliefs, and we explore how this bias affects collective opinion formation. We introduce a model of binary opinion dynamics on a complex, fluctuating network with stochastic rewiring and we analyze these dynamics in the mean-field limit of large networks and fast link rewiring. We show that confirmation bias induces a segregation of individuals with different opinions and stabilizes the consensus state. We further show that bias can have an unusual, nonmonotonic effect on the time to consensus and this suggests a novel avenue for large-scale opinion manipulation.

When opinions, behaviors or ideas diffuse within a population, some are invariably more sticky than others. The stickier the opinion, behavior or idea, the greater is an individual’s inertia to replace it with an alternative. Here we study the effect of stickiness of opinions in a two-opinion model, where individuals change their opinion only after a certain number of consecutive encounters with the alternative opinion. Assuming that one opinion has a fixed stickiness, we investigate how the critical size of the competing opinion required to tip over the entire population varies as a function of the competing opinion’s stickiness. We analyze this scenario for the case of a complete-graph topology through simulations, and through a semi-analytical approach which yields an upper bound for the critical minority size. We present analogous simulation results for the case of the Erdős–Renyi random network. Finally, we investigate the coarsening properties of sticky opinion spreading on two-dimensional lattices, and show that the presence of stickiness gives rise to an effective surface tension that causes the coarsening behavior to become curvature-driven.

We use agent-based modeling to investigate the effect of conservatism and partisanship on the efficiency with which large populations solve the density classification task – a paradigmatic problem for information aggregation and consensus building. We find that conservative agents enhance the populations’ ability to efficiently solve the density classification task despite large levels of noise in the system. In contrast, we find that the presence of even a small fraction of partisans holding the minority position will result in deadlock or a consensus on an incorrect answer. Our results provide a possible explanation for the emergence of conservatism and suggest that even low levels of partisanship can lead to significant social costs.

We study two agent based models of opinion formation—one stochastic in nature and one deterministic. Both models are defined in terms of an underlying graph; we study how the structure of the graph affects the long time behavior of the models in all possible cases of graph topology. We are especially interested in the emergence of a consensus among the agents and provide a condition on the graph that is necessary and sufficient for convergence to a consensus in both models. This investigation reveals several contrasts between the models—notably the convergence rates—which are explored through analytical arguments and several numerical experiments.

We study the voter model with noise on one-dimensional chains using Monte Carlo simulations and finite-size scaling techniques. We observe that the system evolution toward consensus is deeply affected by the addition of noise, and that the time to reach complete ordering increases with the noise parameter q. In particular, the simulations show that the average domain size scales as xi approximately q(-1/2) whereas the magnetization scales with the number of nodes as m approximately N(-1/2).

We study the voter model on heterogeneous graphs. We exploit the nonconservation of the magnetization to characterize how consensus is reached. For a network of N nodes with an arbitrary but uncorrelated degree distribution, the mean time to reach consensus T(N) scales as Nmu(2)1/mu(2), where mu(k) is the kth moment of the degree distribution. For a power-law degree distribution n(k) approximately k(-nu), T(N) thus scales as N for nu > 3, as N/ln(N for nu = 3, as N((2nu-4)/(nu-1)) for 2 < nu < 3, as (lnN)2 for nu = 2, and as omicron(1) for nu < 2. These results agree with simulation data for networks with both uncorrelated and correlated node degrees.

We study the voter model and related random copying processes on arbitrarily complex network structures. Through a representation of the dynamics as a particle reaction process, we show that a quantity measuring the degree of order in a finite system is, under certain conditions, exactly governed by a universal diffusion equation. Whenever this reduction occurs, the details of the network structure and random copying process affect only a single parameter in the diffusion equation. The validity of the reduction can be established with considerably less information than one might expect: it suffices to know just two characteristic timescales within the dynamics of a single pair of reacting particles. We develop methods to identify these timescales and apply them to deterministic and random network structures. We focus in particular on how the ordering time is affected by degree correlations, since such effects are difficult to access by existing theoretical approaches.

We study the viability and resilience of languages, using a simple dynamical model of two languages in competition. Assuming that public action can modify the prestige of a language in order to avoid language extinction, we analyze two cases: (i) the prestige can only take two values, (ii) it can take any value but its change at each time step is bounded. In both cases, we determine the viability kernel, that is, the set of states for which there exists an action policy maintaining the coexistence of the two languages, and we define such policies. We also study the resilience of the languages and identify configurations from where the system can return to the viability kernel (finite resilience), or where one of the languages is lead to disappear (zero resilience). Within our current framework, the maintenance of a bilingual society is shown to be possible by introducing the prestige of a language as a control variable.

We study the opinion dynamics of a generalized voter model in which N voters are additionally influenced by two opposing news sources whose effect is to promote political polarization. As the influence of these news sources is increased, the mean time to reach consensus scales nonuniversally as N^{α}. The parameter α quantifies the influence of the news sources and increases without bound as the news sources become increasingly influential. The time to reach a politically polarized state, in which roughly equal fractions of the populations are in each opinion state, is generally short, and the steady-state opinion distribution exhibits a transition from near consensus to a politically polarized state as a function of α.

We study the nonlinear q-voter model with deadlocks on a Watts–Strogatz graph characterized by two parameters k and β. Using Monte Carlo simulations, we obtain a so-called exit probability and an exit time. We determine how network properties, such as randomness or density of links, influence the exit properties of a model. In particular we show that the exit probability, which is the probability that the system ends up with all spins up, starting with the p fraction of up-spins, has the general form E(p) = pα/(pα + (1 − p)α). Moreover, using the finite-size scaling technique we show that the exit probability exponent α depends both on the parameter q as well as the network structure, i.e. k and β.

We study the influence of complex graphs on the metastability and fixation properties of a set of evolutionary processes. In the framework of evolutionary game theory, where the fitness and selection are frequency dependent and vary with the population composition, we analyze the dynamics of snowdrift games (characterized by a metastable coexistence state) on scale-free networks. Using an effective diffusion theory in the weak selection limit, we demonstrate how the scale-free structure affects the system's metastable state and leads to anomalous fixation. In particular, we analytically and numerically show that the probability and mean time of fixation are characterized by stretched-exponential behaviors with exponents depending on the network's degree distribution.

We study the effect of latency on binary-choice opinion formation models. Latency is introduced into the models as an additional dynamic rule: after a voter changes its opinion, it enters a waiting period of stochastic length where no further changes take place. We first focus on the voter model and show that as a result of introducing latency, the average magnetization is not conserved, and the system is driven toward zero magnetization, independently of initial conditions. The model is studied analytically in the mean-field case and by simulations in one dimension. We also address the behavior of the majority-rule model with added latency, and show that the competition between imitation and latency leads to a rich phenomenology.

We study the dynamics of the voter and Moran processes running on top of complex network substrates where each edge has a weight depending on the degree of the nodes it connects. For each elementary dynamical step the first node is chosen at random and the second is selected with probability proportional to the weight of the connecting edge. We present a heterogeneous mean-field approach allowing to identify conservation laws and to calculate exit probabilities along with consensus times. In the specific case when the weight is given by the product of nodes' degree raised to a power θ, we derive a rich phase diagram, with the consensus time exhibiting various scaling laws depending on θ and on the exponent of the degree distribution γ. Numerical simulations give very good agreement for small values of |θ|. An additional analytical treatment (heterogeneous pair approximation) improves the agreement with numerics, but the theoretical understanding of the behavior in the limit of large |θ| remains an open challenge.

We study the dynamics of the Naming Game (Baronchelli et al. in J Stat Mech Theory Exp P06014, 2006b) in empirical social networks. This stylized agent-based model captures essential features of agreement dynamics in a network of autonomous agents, corresponding to the development of shared classification schemes in a network of artificial agents or opinion spreading and social dynamics in social networks. Our study focuses on the impact that communities in the underlying social graphs have on the outcome of the agreement process. We find that networks with strong community structure hinder the system from reaching global agreement; the evolution of the Naming Game in these networks maintains clusters of coexisting opinions indefinitely. Further, we investigate agent-based network strategies to facilitate convergence to global consensus.

We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power law degree distribution. Application of mean-field theory yields as the main prediction that for symmetric disordered initial conditions the mean time for reaching full order is finite or diverges as a logarithm of the system size N, depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate for describing this problem.

We study an extension to the standard voter model, in which voters have an individual inertia to change their state. We assume that this inertia increases with the time a voter has been in its current state. Increasing the level of inertia in the system decelerates the microscopic dynamics. Counter-intuitively, we find that the time to reach a macroscopic ordered state can be accelerated for intermediate levels of inertia. This is true for different network topologies, including fully-connected ones. We derive a mean-field approach that shows that the origin of this phenomenon is the break of the magnetization conservation because of the evolving inertia. We find that the dynamics near the ordered state is governed by two competing processes, which stabilize either the majority or the minority of voters. If the first one dominates, it accelerates the ordering of the system. PACS 02.50.Ey, 64.60.De, 89.65.-s The voter model [11] has served as a paragon for the emergence of an ordered state in a non-equilibrium system, with numerous inter-disciplinary applications, e.g. in chemical kinetics [10], ecological systems [4, 13, 14, 15], and social systems [3, 8]. It denotes a simple binary system comprised of N voters, each of which can be in one of two states (often referred to as opinions), σi = ±1. The dynamics reads as follows: A voter is selected at random and adopts the state of a randomly chosen neighbor. After N such update events, time is increased by 1. Starting with a random assignment of states to the voters, the key question is then whether the system can reach an ordered state (called consensus) in which all voters have adopted the same σ. The average time Tκ to reach consensus depends (i) on the system size N and (ii) the topology of the network, which recently gained much attention in the physics community [1, 17, 19]. But also the coarsening dynamics in spatially extended systems, i.e. the formation and growth dynamics of state domains was studied and compared to other phase transitions [3, 5, 6]. Among its prominent properties, the magnetization conservation was extensively studied [2, 7, 16, 18]. In this Letter, we extend the standard voter model dynamics by assuming that an individual voter has a certain inertia νi to change its state. νi increases with the persistence time τi which is the time elapsed since the last change of state. The longer the voter already

We study a large family of stochastic processes that update a limited amount in each step. One family of such examples is agent-based modeling, where one agent at a time updates, so the state has small changes in each step. A key question is how this family of stochastic processes is approximated by their mean-field approximations. Prior work shows that the stochastic processes escape repelling fixed points and saddle points in polynomial time. We provide a tight analysis of the above question. For any non-attracting hyperbolic fixed point and a sufficiently small constant ε >0, the process will be ε-far away from the fixed point in O(n log n) time with high probability. We also show that it takes time Ω(n log n) to escape such a fixed point with constant probability. This shows that our result is optimal up to a multiplicative constant. We leverage the above result and show that such stochastic processes can reach the neighborhood of some attracting fixed point in $O(nłog n)$ time with high probability. Finally, We show the power of our results by applying them to several settings: evolutionary game theory, opinion formation dynamics, and stochastic gradient descent in a finite-dimensional space.

We revisit the classical model for voter dynamics in a two-party system with two basic modifications. In contrast to the original voter model studied in regular lattices, we implement the opinion formation process in a random network of agents in which interactions are no longer restricted by geographical distance. In addition, we incorporate the rapidly changing nature of the interpersonal relations in the model. At each time step, agents can update their relationships. This update is determined by their own opinion, and by their preference to make connections with individuals sharing the same opinion, or rather with opponents. In this way, the network is built in an adaptive manner, in the sense that its structure is correlated and evolves with the dynamics of the agents. The simplicity of the model allows us to examine several issues analytically. We establish criteria to determine whether consensus or polarization will be the outcome of the dynamics and on what time scales these states will be reached. In finite systems consensus is typical, while in infinite systems a disordered metastable state can emerge and persist for infinitely long time before consensus is reached.