Construction Of Complex Networks And Analysis Of The Methods Of Evolution

We live in a variety of complex systems. Scholars are committed to study the complexityof complex systems, and some hold the point that the21st century will be the century ofcomplexity. Complex networks provide a good medium to study complexity, the complexityof complex networks is represented by large quantities of nodes and complex relationsbetween nodes.The construction of complex networks in line with the real-world is an importantresearch topic to scholars. The construction of complex networks is started with classicalgraph theory, but it is not complicated enough as the structure of classical graph is simple.The introduction of randomness to construct complex networks has milepost sense; ERrandom graph model is used to simulate real-world complex networks. But the real-worldcomplex networks are not random completely; they have certain rules and features. In the1990s, the small-world network model and the scale-free network model were proposed. Thetwo models are added by certain rules and constraints on the basis of random networks, usingmathematical methods to construct a complex network with certain social laws. Studies haveshown that the real-world complex networks have the features of both small-world andscale-free, how to build complex networks more in line with the real-world has become a hottopic.Different with mathematical methods, this article attempts to construct complexnetworks using an evolutionary method. The evolutionary method constructs complexnetworks by simulating the formation of real social networks. In evolutionary set theory,individuals are organized in the form of sets; individuals are also all connected with eachother in a same set. In the process of evolution, individuals have strategies and gain payoffthough games between individuals, the payoff is translated to fitness and activity of anindividual, individuals learn to update their strategies to adapt to the evolution, the evolutionof network structure is based on operations of adding to sets and quitting from sets, whichpromotes the generation of scale-free feature. Simulation results show that complex networksin line with the real-world can be constructed in an evolutionary method.Besides the construction of complex networks, the article studies the way of evolution.Different evolutionary ways are represented by game models, growth models and themechanisms of network decaying. The prisoner’s dilemma game model and the public goodsgame model are used in the article. Two growth models are fixed population size model andthe incensement of population model. There are two network decaying models, individual decaying model and set decaying model.The article also analyzes the behavior of cooperation between individuals. In awell-mixed population, the probability of interactions between individuals is equal; this maynot guarantee the promotion of cooperation; but in a structured population, behavior ofcooperation can be promoted in certain conditions; for evolutionary set theory, individuals ina same set have higher probability of interaction.The main results of the article are as follows:1. This article presents a model of evolution with complete lifecycle. In this model, thenetwork meets the process of initialization, evolution and decline. Several evolutionary waysare proposed based on the growth of population, the decline mechanisms and the models ofgames.2. The construction of complex networks is based on the analysis of evolutionary ways.According to relevant parameters, we can achieve complex networks which are in line withthe real-world.3. The model studies cooperative behavior between individuals, and verifies that astructured population can promote the behavior of cooperation. If we use the ratio ofcooperation to measure how well a society is, the complex networks that constructed by themodel are all have higher ratios of cooperation and are also positive networks.4. In different network decaying methods and mechanisms of growth of population, thenetwork parameters (clustering coefficient, average shortest path length, degree distribution,etc.) present different characteristics, which is determined by the quality of each model.