Research And Application Of Related Algorithms And Properties Of Multifunctional Complex Networks

The system is called complex system,which is composed of many kinds of subsystems or elements and has complex relationship.Complex system widely exists in the real world,such as celestial system,military system and economic system.Complex network is a high level of abstraction of complex system.By constructing complex network model to analyze complex system,it can reveal the characteristics and evolution law of complex system.At present,researchers have proposed many complex network models based on a large number of data analysis,but most of the models use nodes to represent the individuals and edges to represent the relationship between individuals in the network.The topology of the network is relatively fixed,and the functions of the network are relatively single.The multi-functional complex network(MFCN)model only uses nodes to describe the network,and defines a feature attribute vector for each node.Through the selection of node feature attributes and the definition of corresponding mapping function,different network structures and functions can be realized.However,because the MFCN model does not involve edges,the existing research results are not fully applicable in the MFCN.Therefore,in order to further study and apply the MFCN model to analyze complex systems,the main work of the paper is as follows:1.Combined with the characteristics of the MFCN model,research the search algorithm in MFCN to find the specified content in the network,including neighbor node search,shortest path search,minimum ring search and isomorphic search,and give the relevant definition,algorithm pseudo code and the time complexity analysis.2.Combining the characteristics of the MFCN model,the statistical characteristics of the MFCN are described from the node and network level,including the degree of node,clustering coefficient,centrality,number of rings and ring ratio based on F.The average degree,average clustering coefficient,connectivity,average path length,network efficiency and inter network correlation of the network based on are described.3.Taking China's urban system as an example,the paper applies the MFCN model and the search algorithms and statistical characteristic quantities given in the paper,constructs the urban multi-functional complex network,integrates the attribute analysis and relationship evaluation in urban network research,and comprehensively analyzes the traffic and economic links of China's urban system from multiple perspectives through the actual data.