The Statistical Analysis Of Recommendation Network

The formation and evolution of real networks is not by chance,but follows some certain rules or mechanisms.The purpose of this paper is to study the internal connection rules of a kind of recommendation system,named”Douban Group"linking network,and to explore the underlying global and local connection strategies using a Null-model.Firstly,this paper reviews some recent researches in the field of online social network,and also introduces the development of complex network science and its basic knowledge content.Then,we calculate some topological parameters of"Douban Group"linking network,indicating that the average out-degree is around 8.This mainly results from the spatial limitation of available links in the underlying system.Furthermore,the in-degree distribution is linearly fitted in double logarithmic coordinates.Result shows that there is non-negligible deviation between the empirical data and fitting result when the in-degree is less than 10.This suggests that there is no exponential attenuation for the degree distribution in this period.However,the deviation will decrease with the increase of in-degree.And an obvious”fat tail”phenomenon also appears,which can be eliminate by the cumulative in-degree distribution accompa-nied by a rapid attenuation at the tail.This denotes that"Douban Group"linking network inhibits the emergence of nodes with large in-degrees.Meanwhile,empirical results exhibit a good connectivity in"Douban Group"linking network where most nodes and edges are contained in a connected cluster.Finally,we concern the high-order topological property of"Douban Group"linking network.Its degree correlation and motif structure are systematically ana-lyzed by constructing a Null-model.Results display that there is a significant dif-ference in external connections among nodes with in-degrees respectively located in intervals 0?25,25?60,and 60?160.More specifically,a node of smaller in-degree has larger external connections.It is noted from the fitting results of the excess aver-age degree that a large deviation exists for nodes of in-degrees greater than 80.This suggests the external connections of these nodes do no obviously depend upon node's in-degrees.However,nodes of in-degree changing from 25 to 80 tend to connect to those ones of large in-degree.But the excess average degree of nodes with in-degree between 0 and 25 is warped.This indicates a non-obvious tendency of these nodes to connect to the nodes with greater in-degrees.Constructing a Null-model,we analyze the connection strategy of”Douban Group”linking network.The values of degree correlation explain a strategy of establishing a connection between two nodes of the same in-degree which is less than 60.A different connection strategy appears when the in-degree is larger than 60,where a connection is tended to be established be-tween two nodes of different in-degrees.Furthermore,nodes of in-degree larger than 25 tend to connect to nodes with small in-degrees.The analysis of the motif struc-ture presents the importance of nodes 36 and 166 in the combination of ternary or higher element motifs.It is also noticed that,in "Douban Group"linking network,bidirectional edges are commonly existed in strongly connected subgraphs.