Narrow Results

Opinion formation is a process through which interactions of individuals and dynamism of their opinions in effect of neighbors are modeled. In this paper, in an effort to model the opinion formation more realistically, we have introduced a model that considers the role of network structure in opinion dynamics. In this model, each individual changes his opinion in a way so as to decrease its difference with the opinion of trusted neighbors while he intensifies his dissention with the untrusted ones. Considering trust/distrust relations as a signed network, we have defined a structural indicator which shows the degree of instability in social structure and is calculated based on the structural balance theory. It is also applied as feedback to the opinion formation process affecting its dynamics. Our simulation results show formation of a set of clusters containing individuals holding opinions having similar values. Also, the opinion value of each individual is far from the ones of distrusted neighbors. Since this model considers distrust and instability of relations in society, it can offer a more realistic model of opinion formation.

Social networks have attracted remarkable attention and it is of great importance to understand the process of opinion spreading in popular social networks. However, most research on diffusion cannot be applied directly to investigate social networks, where relationships are heterogeneous and structural balance is a common phenomenon. In this paper, we propose models to characterize the process of opinion spreading in signed social networks under the impact of structural balance. We classify users into different types according to the numbers of their positive links, and define the term user influence to represent the average number of times that users are influenced, which is incurred by a user spreading an opinion. We then propose an approach to analyze the user influence theoretically and the analysis accuracy is verified by simulations. We observe that the user influence increases with user type and also increases with the fraction of negative links in the network if this fraction value exceeds some point. That's to say, negative relationships may enhance opinion spreading if we consider the impact of structural balance, which is an interesting result.

Social networks have attracted remarkable attention from both academic and industrial societies and it is of great importance to understand the formation of social networks. However, most existing research cannot be applied directly to investigate social networks, where relationships are heterogeneous and structural balance is a common phenomenon. In this paper, we take both positive and negative relationships into consideration and propose a model to characterize the process of social network formation under the impact of structural balance. In this model, a new node first establishes a link with an existing node and then tries to connect to each of the newly connected node’s neighbors. If a new link is established, the type of this link is determined by structural balance. Then we analyze the degree distribution of the generated network theoretically, and estimate the fractions of positive and negative links. All analysis results are verified by simulations. These results are of importance to understand the formation of social networks, and the model can be easily extended to consider more realistic situations.

In the existing research results of the complex dynamical networks controlled, the controllers are mainly used to guarantee the synchronization or stabilization of the nodes’ state, and the terms coupled with connection relationships may affect the behaviors of nodes, this obviously ignores the dynamic common behavior of the connection relationships between the nodes. In fact, from the point of view of large-scale system, a complex dynamical network can be regarded to be composed of two time-varying dynamic subsystems, which can be called the nodes subsystem and the connection relationships subsystem, respectively. Similar to the synchronization or stabilization of the nodes subsystem, some characteristic phenomena can be also emerged in the connection relationships subsystem. For example, the structural balance in the social networks and the synaptic facilitation in the biological neural networks. This paper focuses on the structural balance in dynamic complex networks. Generally speaking, the state of the connection relationships subsystem is difficult to be measured accurately in practical applications, and thus it is not easy to implant the controller directly into the connection relationships subsystem. It is noted that the nodes subsystem and the relationships subsystem are mutually coupled, which implies that the state of the connection relationships subsystem can be affected by the controllable state of nodes subsystem. Inspired by this observation, by using the structural balance theory of triad, the controller with the parameter adaptive law is proposed for the nodes subsystem in this paper, which may ensure the connection relationship matrix to approximate a given structural balance matrix in the sense of the uniformly ultimately bounded (UUB). That is, the structural balance may be obtained by employing the controlling state of the nodes subsystem. Finally, the simulations are used to show the validity of the method in this paper.

The structural balance based on the triads structure is used to describe the evolution of the relationships in a social network of humans or animals, where the social network can be abstracted into a complex dynamical network which is composed of the nodes subsystem (NS) and the connection relationships subsystem (CS) coupled with each other. Similar to the synchronization or stabilization in NS with the help of CS, structural balance may be arrived at in CS with the help of NS. In this paper, the CS is described by the Riccati linear matrix differential equation with dynamical coupling term, only including the internal states of the NS. We mainly focus on the dynamic behaviors of NS which can lead to the structural balance in CS. It has been proved under some mathematical conditions that if the NS converges to some nonzero constant targets via the adaptive decentralized control scheme for each node, then the CS will asymptotically track a certain structural balance via the effective coupling. Such a result can be used as a specific explanation for the relationship between the structural balance and the dynamic changes of the nodes’ states. Finally, the simulation example is given to show the validity of the method in this paper.

In social networks, individuals are usually but not exactly divided into communities such that within each community people are friendly to each other while being hostile towards other communities. This is in line with structural balance theory which enables a comprehensive understanding of the stability and tensions of social systems. Yet, there may be some conflicts such as the intra-community negative edges or inter-community positive edges that affect the balancedness of the social system. This raises an interesting question of how to partition a signed network for minimal conflicts, i.e., maximum balancedness. In this paper, by analyzing the relationship between balancedness and spectrum space, we find that each eigenvector can be an indicator of dichotomous structure of networks. Incorporating the leader mechanism, we partition signed networks to maximize the balancedness with top-k eigenvectors. Moreover, we design an optimizing segment to further improve the balancedness of the network. Experimental data both from real social and synthetic networks demonstrate that the spectral algorithm has higher efficiency, robustness and scientificity.

This paper is concerned with the structural balance problem for complex dynamical network with the help of coupling effect related to the external stimulations. Consider a network with time-varying and value-weighted links, which can be regarded as a dynamic system. The link dynamic system is modeled as a Riccati matrix difference equation with the coupling matrix related to the external stimulations. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive a simple criterion for ensuring that the discrete link system asymptotically achieves structural balance, meanwhile, the external stimulations track a corresponding vector signal as well. Simulation examples are given to demonstrate the usefulness of the proposed control scheme in this paper.

Recently, problems related to structural balance have received widespread attention in the research fields of signed networks, such as signed network partition, community detection and correlation clustering. Structural balance problems aim to find a partition of a signed network such that the frustration index, the sum of positive edges between subsets and negative edges within subsets, is minimized, which is known to be nondeterministic polynomial-time (NP)-complete and remains an open challenge. Many heuristic and meta-heuristic algorithms are developed to minimize the frustration index. However, most extant algorithms require quite a few parameters and are not efficient enough for large signed networks. In this study, we present a simple and effective iterated greedy (IG) algorithm for solving the structural balance problems with the objective of frustration minimization. In the algorithm, a constructive greedy heuristic is proposed to generate and reconstruct solutions to the problem with high efficiency. A two-stage local search procedure is designed to exploit the search space at different levels of granularity. An adaptive destruction method is developed to enhance the exploitation ability of the algorithm in the early stage and maintain the exploration ability later. Additionally, two acceleration methods are proposed to help the algorithm get a better performance in large signed networks. The experimental results indicate that the proposed IG algorithm outperforms other meta-heuristics in the literature especially in terms of the computational time.

This paper studies the stabilization problem of complex dynamical networks with nonlinear similar nodes and arbitrary finite communication delays, while the networks are structural balance. For the considered networks, the information flow is undirected or directed, and only locally delayed information can be used for each node. We derive that stabilization of structurally balanced networks can be realized by designing decentralized controllers, when the associated assumptions are true. Furthermore, the proposed stabilization schemes are also useful to the structurally balanced networks without communication delays. Finally, the simulations are presented to show the effectiveness of the method in this paper.

This paper investigates the adaptive structural balance control of complex dynamical networks by employing the controlled external stimulus signals which are coupled and transmitted to the dynamics of complex dynamical network. The control objective is to assure the asymptotical convergence of the dynamical links to the structural balance by the controlled external stimulus signals. The dynamical links of complex dynamical network are represented in this paper mathematically as the Riccati matrix differential equation with the controlled external stimulus signals which are coupled approximately in the form of Hebb rule. Compared with the existing results which are mainly concerned with the dynamical characteristics of nodes such as synchronization, this paper is mainly focused on the dynamical characteristic of links so named as the structural balance which is asymptotically obtained by the adaptive control scheme of external stimulus signals. Finally, a simulation example is given to show the validity of result proposed in this paper.

In this paper, the discrete-time complex dynamical networks with dynamic weighted value of connection relationships are regarded to be composed of the node and link subsystems, and the state variables of the two subsystems are mutually coupled. Different from most of the existing researches on synchronization or stabilization of nodes, the emphasis of this paper is on the links instead of nodes. This paper mainly focuses on the generation mechanism of structural balance in the link subsystem, the nodes only play an auxiliary role. Associated with the dynamic coupling term in the link subsystem, the suitable controller is proposed for node subsystem such that the structural balance of link subsystem without control input be achieved indirectly. Finally, a numerical simulation is given to show the effectiveness of the method in this paper.

This article explains a simulation of the Co-Author Model (CAM) applied in strategic alliance setting where firms use and optimize their network resources. To understand its process casualty better, I explain the model's mechanisms in terms of its interactive dynamics and resulting equilibrium structure. Classified as a Boolean network with two inputs, CAM's dynamics cause a biased equilibrium structure that could then be explained by the Simmelian tie and the completion of structure through structural balance. These explanations not only could answer the criticism that a simulation model is merely a toy model without much realism but could also explain and give insights to both substantive theory and methodology development in strategic alliance research. The results include the effect of a third party, the embeddedness of firms in their alliances, and the real-world implications of the "frozen web": a phenomenon drawn parallel to the financial crisis beginning in 2007.

Resilience denotes the capacity of a system to withstand shocks and its ability to recover from them. We develop a framework to quantify the resilience of highly volatile, non-equilibrium social organizations, such as collectives or collaborating teams. It consists of four steps: (i) delimitation, i.e. narrowing down the target systems, (ii) conceptualization, i.e. identifying how to approach social organizations, (iii) formal representation using a combination of agent-based and network models, (iv) operationalization, i.e. specifying measures and demonstrating how they enter the calculation of resilience. Our framework quantifies two dimensions of resilience, the robustness of social organizations and their adaptivity, and combines them in a novel resilience measure. It allows monitoring resilience instantaneously using longitudinal data instead of an ex-post evaluation.

The notion of corona of two graphs was introduced by Frucht and Harary in 1970. In this paper, we generalize their definition of corona product of two graphs and introduce corona product of two signed graphs by utilizing the framework of marked graphs, which was introduced by Beineke and Harary in 1978. We study structural and spectral properties of corona product of signed graphs. Further, we define signed corona graphs by considering corona product of a fixed small signed graph with itself iteratively, and we call the small graph as the seed graph for the corresponding corona product graphs. Signed corona graphs can be employed as a signed network generative model for large growing signed networks. We study structural properties of corona graphs that include statistics of signed links, all types of signed triangles and degree distribution. Besides we analyze algebraic conflict of signed corona graphs generated by specially structured seed graphs. Finally, we show that a suitable choice of a seed graph can produce corona graphs which preserve properties of real signed networks.