For Local Optimal Complex Network Modeling

There are many kinds of complex systems, which can be depicted as complexnetworks, in nature world and human society. Complex networks are widely used inmany fields such as communications, society, engineering technology and management.Complex networks, one of the hot spots in academic research, promote studies ofcomplex systems immensely. Opening up a new prospect in the study of economics andmanagement, complex networks have been applied to such aspects as informationpropagation and exchange, viral marketing, dynamic decision, supply chainmanagement, sampling strategy and so on. The rules of complex network, however,have not yet unclosed. Analyzing the topology of complex networks mathematically hasnot only academic significance but also further applied potentials. In this thesis,topologies of real-life systems are simulated via building network models, thenanalyzing their properties. Main results are as following:1. A deterministic network with first-mover advantages is proposed. Nodes’ statusesare depicted by node degree and strong nodes have large degree. A deterministicnetwork model, in which new nodes have different statuses, is presented. By classicalprobability, the degree distribution is calculated. The relevant network parameters areanalyzed. The network is a scale-free hierarchical one with fractal property and thefractal dimension is equal to the power-law exponent. BA scale-free network displaysfirst-mover advantages. In our network, the earlier a node was created, the larger degreeit has. Regarding node degree as capacity, ability or social relations individual possesses,earlier nodes have large degree just corresponds with take precedence, that isfirst-mover advantages.2. To explore methods to calculate the degree distribution of growth networks.Basing on thoughts of the customer input process in random service system, nodesincoming is considered as a random process. A general random-growth-network modelis presented and its stationary degree distribution is analyzed by the random processtheory. The method is a short-cut one, with the boarder scope of application, and can bedisplay the “Success to the Successful” phenomenon in the scale-free network.3. The power-law exponent of non-stationary growth networks is discussed. Tosimulating some information networks, a directed network model with logarithmaccelerating growth of edges, a directed network model with exponent accelerating growth of edges and a network model with exponent accelerating growth of nodes ispresented. Then the degree distribution of the directed network model with logarithmaccelerating growth of edges is analytically obtained. The corresponding relationsbetween accelerating growth of non-stationary growth networks and its degreedistribution exponents are discussed. It is founded that the power-law degree exponentchanges in a negative direction with the accelerating growth.4. A local attachment network model is presented. In many real-life networks,incomers may only connect to a few others in a local area because of their limitedability or information, and individuals in a local area are likely to have close relations.Accordingly, we propose a local-attachment-network model. Here, a local area networkstands for one constructed by a node and all its neighbors. The new nodes performnonlinear preferential attachment in local areas. Main quantities are calculated insimulation and the degree distribution and clustering-degree correlations are analyticallyobtained. The model can generate different kinds of degree distributions by adjustingthe parameter. And the network displays the hierarchical organization independent ofthe parameter. In two aspects, the complex network and the social network analysis,features of our network are gained comparatively.