| Complex network theory provides a new insight into abstracting and simplifying real-world complex systems.It abstracts the complex system in the real world as a network consisting of nodes and the links between nodes.The relevant laws of complex systems are understood by analyzing the structure and functions of the network,and the stability of complex systems is regulated by using the control theory in complex network,which have important theoretical significance and application value for the design of complex systems in the real world.Modeling features of complex networks is the foundation for understanding the structure and functions of the network,and is also the basis for applying complex networks to solve problems in real-world complex systems.Recent studies have indicated the dependency between network features and the network stability,and also have showed the constraint of resource costs for the network stability.It is noticeable that the improvement of network stability will increase resource costs.Therefore,it is worth studying how to achieve a balance between resource costs and the network stability,and the relationship between the balanced results and network features.This paper establishes a multi-objective optimization model with stability and resource costs as the optimization objectives.By the proposed model,the origins of network features and the relationship among the features can be studied.Further,we extend the proposed model to study the origins of community structure,and study the information spreading and algorithms on networks with different features generated by the proposed dual-optimal model.The main content of this dissertation is as follows.(1)There exist dependent and constrained relationship among three entities-net-work features,resource costs,and network stability.However,most of current research-es study the three entities independently,or only study the relationship between the two of them.In addition,current studies cannot use few parameters to explain the origin of various network features in one model.Regarding the maximization of the network stability(edge degree of the network)and the minimization of the resource costs(the node degree of the network)as the optimization objectives,constrained by the average shortest path length,this paper proposes a dual-optimal model that can describe a variety of network features to achieve a dynamic equilibrium.Theoretical proof and experimental results show that the model can generate complex networks with multiple features,including scale-free,small-world,ultra-small-world,compact,Delta-distribution,regular and random networks.Moreover,the proposed model obtains a schematic map of network features,and the map expresses the relationship between the features of networks.In addition,the dual-optimal model draws a different conclu-sion compared with the current one:it is widely believed that hub repulsion results in the emergence of fractal feature,but the results of the dual-optimal model show that hub-hub attracted network also can be fractal.These results provide new thoughts for the further study of the community structure,the algorithm on the hub-hub attracted fractal network,and information spreading on networks with different features.(2)There exist different viewpoints for the origin of community structure,this paper proposes a community-structure and scale-free network optimization model based on the dual-optimal model,and we find that“similarity distance”is the origin.This paper adds the constraint“similarity distance”to the dual-optimal model,and then studies the relationship between the two constraints and the optimization results.The results show that“similarity distance”is the origin of community structure.Moreover,the proposed model can simulate the real-world community-structure scale-free network more accurately than the current models.In addition,the model can cover the current typical community-structure models.(3)The traditional box-covering method is difficult to obtain the optimal number of boxes on the hub-hub attracted fractal network,thus a more accurate box-covering algorithm is needed to optimize the number of boxes;in addition,many studies show that optimizing the number of boxes can ensure the maximum of fractal modularity,but this conclusion is not always valid.To solve the two mentioned problems,this paper presents a multi-objective particle swarm based box-covering method to solve the two difficulties simultaneously.The proposed algorithm satisfies both the goals of minimizing the number of boxes and maximizing the fractal modularity.The proposed algorithm uses Chebyshev's method for multi-object decomposition,and the solutions are obtained based on the framework of discrete particle swarm optimization algorithm.Experimental results show that the proposed algorithm achieves 100%improvement for the optimization of fractal modularity compared with the traditional box-covering method,when the number of boxes is minimized.The lowest average improvement reaches 25%.Moreover,the proposed algorithm has a better convergence than other algorithms applied in the paper.(4)Current researches usually studies information propagation on networks with different network size and different attributes.Therefore,it is impossible to confirm whether network types or network attributes are key factors affecting information d-iffusion.The simple and effective strategy to solve this problem is to use the control variable method as experimental network sets.Therefore,this paper generates network dataset with different type based on the dual-optimal model.Experimental results show that the average shortest distance of the network has the greatest impact on information spreading compared t.o network type,clustering coefficient,and assortativity coefficien-t.Moreover,the shorter the average shortest path length is,the larger the spreading efficiency will be.Further,this dissertation studies the information spreading in the real world based on the obtained conclusion.Since the credibility of individuals in social networks plays a.n important role for others to believe and spread a piece of informa-tion,we propose a information spreading model based on the trust of individuals.The establishment of trust and the information spreading process can take place in different social circumstances,so we set the model working on multiple networks.The experi-mental results show that the information spreads more efficiently on random network and DSF network with the shortest path length.Moreover,increasing the influence of the trustable state will improve information spreading. |
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