Research On Multi-functional Complex Network Model And Its Related Properties

With the advent of data age,a large number of complex systems in reality can be described abstractly through complex networks and applied to various fields of different disciplines,such as the relationship map in social networks,the traffic network in urban planning,the molecular model in bioengineering,etc.In the existing complex network model,nodes are used to represent different individuals of the real system,while edges are used to represent the relationship between individuals.In complex networks nodes can have multiple attributes,and different attributes or attribute sets will lead to different connections between nodes,thus the network would have different functions.Aiming at the problem that existing complex network models can not construct networks with different functions according to the selected attributes of nodes,multifunctional complex network model is proposed.The complex network model provides a method to depict different topological structures and network functions of complex systems with different and multi-attribute elements from attribute perspectives,which makes the analysis of complex system network get new research ideas.The main work and major research achievements are as follows:1.Definition of multi-functional complex network model.The network model is represented only by nodes and their attribute sets.Different network topology and network functions are determined by selecting the attributes of nodes and defining the mapping rules of nodes under the corresponding attributes.By establishing and analyzing a missile defense network and city network in the middle reaches of the Yangtze River,the availability and effectiveness of the multi-functional complex network model are verified.2.Research on the topological properties of multi-functional complex network model.The topological properties of the multi-functional complex network model based on the characteristic attributes are given from the aspects of node properties,network properties and centrality measurement,including the degree and weight of nodes,the clustering coefficient of nodes,the accessibility between nodes,the connectivity of networks,the path length of networks,the degree centrality,the closeness centrality,the betweenness centrality,etc.3.Research on k-step Topological properties of network based on multi-functional complex network model.Considering the characteristics of multi-functional complex network model,the k-step reachability query algorithm based on the model is proposed.Furtherly,the paper also completes the transformation between the relational data and the multi-functional complex network model from the attribute dimension,and realizes the k-step reachability query of the multi-functional complex network model.