Analysis for the Topology of Complex Networks: In Theory and Simulation
|School||Central South University|
|Course||Probability Theory and Mathematical Statistics|
|Keywords||Degree distribution Degree of correlation Aggregation Markov Chain The power-law distribution|
Complex network able to describe a very wide range of natural and social systems, and in recent years has become an emerging field of research on a very impressive this thesis, starting from probability theory, graph theory and statistical physics point of view, the system complex network some important topological characteristics of the main research work as follows: the first chapter introduces the research background, preparatory knowledge and this paper's main work in the second chapter, from the point of view of probability theory, discussion of a complex network stable the attitude distribution Existence and related issues. networking Markov chain according to the definition and nature of the complex network, and thus the use of the methods and techniques of the first passage probability theory of Markov chains to provide a rigorous proof for the existence of the growth distribution network stable attitude. The paper first analyzes allow reconnection classic model - DMS model provides a rigorous proof of the existence of the distribution for the network stable attitude. further explore a class of general network model - Fixed Cooper-Frieze model We prove the existence of the model is stable attitude distribution, through numerical simulation, the degree distribution and aggregation of the model and BA model comparison analysis. third chapter, the main research groups preferential model some important topological characteristics and simulation analysis. the group preferential model for the study of complex networks to introduce a new merit-based thinking - groups merit-based thinking. discussed two types of groups preferred model - no right groups preferred model and weighted groups preferential model topology characteristics and synchronization analysis First, no right groups preferential model, our utilization equation method analyzes its degree distribution, correlation and aggregation, and in this paper, we provide a wide range of simulation analysis for the model and draw simulation results is fully consistent with the analytical results. Secondly, the selection of the best model of weighted groups we mainly analyze its degree distribution, point rights and edge right distribution, research groups, merit-based thinking in the evolution process of weighted network topology, and results BBV model made a comparative analysis. addition, we further preferential model of groups made simultaneous analysis of, and discuss the synchronization capabilities of the network in the case of random failures and malicious attacks. articles in the last two chapters, the main use of complex network of research methods, made some applications on social networks and natural network analysis, which in the fourth chapter, we study the wealth of the topology of the network model and the distribution of wealth. according to the characteristics of the economic relations between the social individuals and organizations through to consider wealth Reclassification and merit-based mechanisms, and other factors impact on the network structure, we have established a the wealth network model. emphasized, considering the network model of the two types of wealth, which was theoretically the degree distribution model and some other important topological characteristics research and simulation analysis In the fifth chapter, we study the topology of the network model of a class of biological structure and function, we propose a new class of protein domain interaction network model through the introduction of a new merit-based thinking and evolution mechanism. Meanwhile, the main research class protein domains interacting some important topological features of the network, such as the degree distribution, aggregation, and the shortest path length, etc..