Network Characteristics Analysis In Several Network Generation Models

The real world is full of various complex networks,such as information networks,communication networks,biological networks,social networks.However,social net-working is a double-edged sword:it brings great convenience to our lives,yet negative effects may also arise.For example,infectious diseases can spread around the world more easily through the transportation network.Regarding the wide influence of the network,a more comprehensive,incisive,and systematic study of the networking is urgently needed.Therefore,network science research is becoming more and more sig-nificant.It is an important approach to to analyze network data by studying the charac-teristics of the network.By employing the main characteristics of the network,the underlying laws and mechanisms of the network can be clearly recognized,common ground between various complex networks as well as common methods for analyzing them can be determined,and various practical network problems can be dealt with.At present,most studies on network characteristics focused on data-based descriptive analysis,where the characteristics cannot be given a clear description.Besides,the data tended to be random,which is not conducive to our overall understanding of the network characteristics.In this thesis,the quantitative description of its overall distribution was abstract-ed based on the original qualitative description of network reciprocity,transitivity and within-node dependence.In particular,reciprocity and transitivity were defined in the case of discrete and continuous networks.Furthermore,the specific forms of these characteristics in the ER random graph model,stochastic block model and two-way factor analysis model were also analyzed and their properties are studied based on the definition of these network characteristics on the whole.Finally,numerical simulations were designed to verify the main conclusions that we have obtained,then example data were analyzed to illustrate the validity and rationality of the quantitative description of these network characteristics.