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In this work, we investigate a heterogeneous population in the modified Hegselmann-Krause opinion model on complex networks. We introduce the Shannon information entropy about all relative opinion clusters to characterize the cluster profile in the final configuration. Independent of network structures, there exists the optimal stubbornness of one subpopulation for the largest number of clusters and the highest entropy. Besides, there is the optimal bounded confidence (or subpopulation ratio) of one subpopulation for the smallest number of clusters and the lowest entropy. However, network structures affect cluster profiles indeed. A large average degree favors consensus for making different networks more similar with complete graphs. The network size has limited impact on cluster profiles of heterogeneous populations on scale-free networks but has significant effects upon those on small-world networks.
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Opinion formation is an important element of social dynamics. It has been widely studied in the last years with tools from physics, mathematics and computer science. Here, a continuous model of opinion dynamics for multiple possible choices is analysed. Its main features are the inclusion of disagreement and possibility of modulating information, both from one and multiple sources. The interest is in identifying the effect of the initial cohesion of the population, the interplay between cohesion and information extremism, and the effect of using multiple sources of information that can influence the system. Final consensus, especially with external information, depends highly on these factors, as numerical simulations show. When no information is present, consensus or segregation is determined by the initial cohesion of the population. Interestingly, when only one source of information is present, consensus can be obtained, in general, only when this is extremely mild, i.e. there is not a single opinion strongly promoted, or in the special case of a large initial cohesion and low information exposure. On the contrary, when multiple information sources are allowed, consensus can emerge with an information source even when this is not extremely mild, i.e. it carries a strong message, for a large range of initial conditions.
In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks.
Here we developed a new conceptual, stochastic Heterogeneous Opinion-Status model (HOpS model), which is adaptive network model. The HOpS model admits to identify the main attributes of dynamics on networks and to study analytically the relation between topological network properties and processes taking place on a network. Another key point of the HOpS model is the possibility to study network dynamics via the novel parameter of heterogeneity. We show that not only clear topological network properties, such as node degree, but also, the nodes status distribution (the factor of network heterogeneity) play an important role in so-called opinion spreading and information diffusion on a network. This model can be potentially used for studying the co-evolution of globally aggregated or averaged key observables of the earth system. These include natural variables such as atmospheric, oceanic and land carbon stocks, as well as socio-economic quantities such as global human population, economic production or wellbeing.
To understand, predict, and control complex networked systems, a prerequisite is to reconstruct the network structure from observable data. Despite recent progress in network reconstruction, binary-state dynamics that are ubiquitous in nature, technology and society still present an outstanding challenge in this field. Here we offer a framework for reconstructing complex networks with binary-state dynamics by developing a universal data-based linearization approach that is applicable to systems with linear, nonlinear, discontinuous, or stochastic dynamics governed by monotonous functions. The linearization procedure enables us to convert the network reconstruction into a sparse signal reconstruction problem that can be resolved through convex optimization. We demonstrate generally high reconstruction accuracy for a number of complex networks associated with distinct binary-state dynamics from using binary data contaminated by noise and missing data. Our framework is completely data driven, efficient and robust, and does not require any a priori knowledge about the detailed dynamical process on the network. The framework represents a general paradigm for reconstructing, understanding, and exploiting complex networked systems with binary-state dynamics.
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