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This paper examines the interplay of opinion exchange dynamics and communication network formation. An opinion formation procedure is introduced which is based on an abstract representation of opinions as $k$--dimensional bit--strings. Individuals interact if the difference in the opinion strings is below a defined similarity threshold $d_I$. Depending on $d_I$, different behaviour of the population is observed: low values result in a state of highly fragmented opinions and higher values yield consensus. The first contribution of this research is to identify the values of parameters $d_I$ and $k$, such that the transition between fragmented opinions and homogeneity takes place. Then, we look at this transition from two perspectives: first by studying the group size distribution and second by analysing the communication network that is formed by the interactions that take place during the simulation. The emerging networks are classified by statistical means and we find that non--trivial social structures emerge from simple rules for individual communication. Generating networks allows to compare model outcomes with real--world communication patterns.
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In Hopfield neural networks with up to 10^8 nodes we store two patterns through Hebb couplings. Then we start with a third random pattern which is supposed to evolve into one of the two stored patterns, simulating the cognitive process of associative memory leading to one of two possible opinions. With probability p each neuron independently, instead of following the Hopfield rule, takes over the corresponding value of another network, thus simulating how different people can convince each other. A consensus is achieved for high p.
In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentially between interactions. Specifically, we formulate continuous-time Laplacian dynamics and a discrete-time DeGroot model of opinion dynamics on these tie-decay networks, and we carry out numerical computations for the continuous-time Laplacian dynamics. We examine the speed of convergence by studying the spectral gaps of combinatorial Laplacian matrices of tie-decay networks. First, we compare the spectral gaps of the Laplacian matrices of tie-decay networks that we construct from empirical data with the spectral gaps for corresponding randomized and aggregate networks. We find that the spectral gaps for the empirical networks tend to be smaller than those for the randomized and aggregate networks. Second, we study the spectral gap as a function of the tie-decay rate and time. Intuitively, we expect small tie-decay rates to lead to fast convergence because the influence of each interaction between two nodes lasts longer for smaller decay rates. Moreover, as time progresses and more interactions occur, we expect eventual convergence. However, we demonstrate that the spectral gap need not decrease monotonically with respect to the decay rate or increase monotonically with respect to time. Our results highlight the importance of the interplay between the times that edges strengthen and decay in temporal networks.
We present a general framework for the study of coevolution in dynamical systems. This phenomenon consists of the coexistence of two dynamical processes on networks of interacting elements: node state change and rewiring of links between nodes. The process of rewiring is described in terms of two basic actions: disconnection and reconnection between nodes, both based on a mechanism of comparison of their states. We assume that the process of rewiring and node state change occur with probabilities Pr and Pc respectively, independent of each other. The collective behavior of a coevolutionary system can be characterized on the space of parameters (Pr, Pc). As an application, for a voterlike node dynamics we find that reconnections between nodes with similar states lead to network fragmentation. The critical boundaries for the onset of fragmentation in networks with different properties are calculated on this space. We show that coevolution models correspond to curves on this space describing functional relations between Pr and Pc. The occurrence of a one-large-domain phase and a fragmented phase in the network is predicted for diverse models, and agreement is found with some earlier results. The collective behavior of system is also characterized on the space of parameters for the disconnection and reconnection actions. In a region of this space, we find a behavior where different node states can coexist for very long times on one large, connected network.
In this paper, we propose a generalized opinion dynamics model (GODM), which can dynamically compute each persons expressed opinion, to solve the internal opinion maximization problem for social trust networks. In the model, we propose a new, reasonable and interpretable confidence index, which is determined by both persons social status and the evaluation around him. By using the theory of diagonally dominant, we obtain the optimal analytic solution of the Nash equilibrium with maximum overall opinion. We design a novel algorithm to maximize the overall with given budget by modifying the internal opinions of people in the social trust network, and prove its optimality both from the algorithm itself and the traditional optimization algorithm-ADMM algorithms with $l_1$-regulations. A series of experiments are conducted, and the experimental results show that our method is superior to the state-of-the-art in four datasets. The average benefit has promoted $67.5%$, $83.2%$, $31.5%$, and $33.7%$ on four datasets, respectively.
In this work we study the opinion evolution in a community-based population with intergroup interactions. We address two issues. First, we consider that such intergroup interactions can be negative with some probability $p$. We develop a coupled mean-field approximation that still preserves the community structure and it is able to capture the richness of the results arising from our Monte Carlo simulations: continuous and discontinuous order-disorder transitions as well as nonmonotonic ordering for an intermediate community strength. In the second part, we consider only positive interactions, but with the presence of inflexible agents holding a minority opinion. We also consider an indecision noise: a probability $q$ that allows the spontaneous change of opinions to the neutral state. Our results show that the modular structure leads to a nonmonotonic global ordering as $q$ increases. This inclination toward neutrality plays a dual role: a moderated propensity to neutrality helps the initial minority to become a majority, but this noise-driven opinion switching becomes less pronounced if the agents are too susceptible to become neutral.
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