Study And Application On The Dynamical Characteristics Of Structural Balance On Complex Networks

As the substrates of relations among individuals, social networks are used to characterize the interactions occur in the social system. However, many social networks of interest include explicit sentiments of social agents towards each other. The structural balance and cognitive dissonance theory provide the way how to evaluate the structure of network by these sentiments.In this thesis, several types of network models (Growing scale-free network, Barabasi-Albert scale-free network, Watts-Strogatz small world network, and Erdos-Renyi random network), are employed to study the dynamics of structural balance of networks. Specifically, three problems are considered in the process of structural balancing, i.e., constrained relation balance, majority-friends rule in the coevolution of opinion propagation and sentimental relations and the coevolution dynamics of opinion propagation and sentimental relations caused by cognitive dissonance. It is found from numerical simulations and theoretical analysis that, the networks exhibit diverse dynamical behaviors in the process of structural balancing. As follows:1. In the constrained relation balance process, it is found that the system ultimately evolves into three absorbing states (i.e. steady state, dynamic balance state, jammed state). The probability of three states occurred and the time reaching absorbing states is strongly affectted by clustering coefficient of networks, while the balance degree of dynamic balance state and jammed state is dramatically related to clustering coefficient.2. By studying the dynamical behaviors of the majority-friends-rule coevolution, it is found that1) the balance degree of the evolved networks is proportional to the structural factors (i.e. the average degree, the initial negative proportion), and it is inversely proportional to the dynamical factors (the probability of updating opinion, the probability of updating all relations);2) The convergence time is proportional to the average degree and inversely proportional to the initial negative proportion and the influence degree of both are equivalent; While the convergence time is proportional to the probability of updating opinion. However it is inconsistent to the probability of updating all relations affected by the probability of updating opinion in different intervals, and the probability of updating all relations effects weaker on the convergence time than the probability of updating opinion does. Moreover, by studying opinion clusters in this section, it is found that the number and size of opinion clusters are strongly affected by the structural factors and dynamical factors. 3. By studying the dynamical behaviors of the coevolution of the cognitive dissonance and structural balance, it is found that1) the balance degree of evolved network increase with tolerance degree of vertices. Meanwhile, the tolerance degree has a threshold and it exerts effects on the balance degree of network only when it is larger than the threshold.2) On three kinds of networks (i.e. Watts-Strogatz network, Barabasi-Albert network, and Erdos-Renyi network), the time of opinions propagating and the time of relations evolving both decrease as tolerance degree rising in general trend. On Watts-Strogatz and Barabasi-Albert networks, time difference between them also decrease with tolerance degree increasing. Firstly, positive time difference implies that opinions propagating speed is faster than that of relation evolving, and then negative time difference shows that the latter is faster than the former. However, on Erdos-Renyi network, the time difference increases in the beginning of the tolerance intervals then keeps stable in the other intervals. And it is always negative to reveal evolving speed is faster than propagating speed from beginning to end.The studies of the second and third process also indicate the analogs of coevolving on Watts-Strogatz and Barabasi-Albert networks and differences between on Erdos-Renyi network and on Watts-Strogatz and Barabasi-Albert networks.This research not only contributes to successfully measure the structural balance of networks by the sentiments included in the networks, but also to figure out the effects of several factors, especially key factors, during the three different dynamical processes. On the one hand, it lays the foundation for studying the structural balance of actual networks; on the other hand it provides methods and datum to control the structural balance of networks in the next step.