Research On The Topological Properties Of Complex Networks And The Application In Hefei Subway Network

In the perspective of network science,complex networks can be understood as mathematical models of complex systems based on data,and they simplify complex systems to abstract structures that only retain the characteristics of basic connection patterns,and establish complex network models.An important goal of statistical research is to combine statistical methods in reality,and to infer the essence of the measured object by analyzing and mining the common topological and statistical properties of different complex networks.We mainly study the topological properties of complex networks and the application in Hefei subway network,innovatively analyze the topological properties of different complex networks from the perspective of theoretical complex networks and real complex networks,combine mathematical and statistical methods,and explore the intrinsic occurrence law and essential characteristics of different networks and draw relevant conclusions.The specific contents are as follows:Firstly,we introduce a family of nested weighted n-polygon networks.We study the coherence of the networks with recursive features that contain the initial states dominated by a weighted parameter.The precise results of first-and second-order coherence are further derived,and the influence of different parameters on coherence is obtained.In addition,it is found that the Laplacian energy increases linearly with the strengthening of first-order coherence,and the expressions of Kirchhoff index,average first-pass time,and network average path length are obtained.These findings will provide a reference for other network coherence studies and a decision-making basis for real network robustness studies.Secondly,we propose a new class of fractal hierarchical networks with a triangular structure,and also discover some unique properties of the network.The average degree and density of the network are derived,so as to prove that the network is sparse,and the degree distribution of hub nodes and bottom nodes of the network are demonstrated respectively,and it is found that hub nodes obey the power law distribution,and bottom nodes are exponentially distributed,so as to derive that the network has scale-free feature.It is found that when the number of iteration steps reaches a certain value,the clustering coefficient with the deterministic duplicates tends to be stable at a positive boundary,and the average path length also increases with the logarithmic increase of the total number of nodes,which judges that the network has a small-world effect.These research results can provide a selection basis for the construction of network models in real systems,and provide more possibilities for the development and application of hierarchical networks.Finally,we use the method of Space L to construct a model of the Hefei subway network based on the theory of complex networks.Taking degree,degree distribution,shortest path length,et al.as the basic topological property characterization indexs,betweenness centrality,closeness centrality,eigenvector centrality and Page Rank value as the importance characterization indicators of nodes,network efficiency,maximum connectivity subgraph,and natural connectivity as structural stability characterization indexes so as to construct the network structure index system and analyze the characteristics of network topology comprehensively.It is found that Hefei subway network has the characteristics of small world effect and scale-free feature,and the importance of the transfer stations and adjacent stations is high,and the ability to resist in the face of different external attacks is strong or weak.At last,we obtain relevant conclusions and suggestions for future development of Hefei’s subway network.