大数据背景下一类社会网统计性质的初步研究
|
摘要
在大数据背景下,文章实证地研究了一类合作竞争网络的集群系数对顶点度的依赖关系,结果显示两者的依赖关系函数c(k)形式是多样的,有指数形式、泊松形式和幂律形式。通过广义合作网络模型,在项目大小分布分别是指数分布、泊松分布和幂律分布的三种情况下,数值模拟了集群系数对顶点度的依赖关系。得到的结果与实证统计的结果相同,即c(k)有指数形式、泊松形式、幂律形式及SPL等多种形式,并得出随机选择旧节点连接的概率p越大,所得网络的集群系数对顶点度的依赖关系越远离幂律形式,越接近均匀情况即指数形式或者泊松形式。
In the background of large data, this paper empirically studies the dependency of clustering coefficient on the degree of a vertex in a class of cooperative competition network. The results show that the dependency function c(k) of the two has various forms, such as exponential form, Poisson form and power law form. Based on the generalized cooperative network model, the dependence of cluster coefficients on vertex degree is numerically simulated in three cases: exponential distribution, Poisson distribution and power law distribution. The results are the same as those of empirical statistics, that is, c(k) has many forms, such as exponential form, Poisson form, power law form and SPL. The greater the probability P of random selection of old node connections, the farther the dependence of cluster coefficients on vertex degree of the network is from the power law form, but the closer to the uniform situation, i.e. exponential form or Poisson form.
In the background of large data, this paper empirically studies the dependency of clustering coefficient on the degree of a vertex in a class of cooperative competition network. The results show that the dependency function c(k) of the two has various forms, such as exponential form, Poisson form and power law form. Based on the generalized cooperative network model, the dependence of cluster coefficients on vertex degree is numerically simulated in three cases: exponential distribution, Poisson distribution and power law distribution. The results are the same as those of empirical statistics, that is, c(k) has many forms, such as exponential form, Poisson form, power law form and SPL. The greater the probability P of random selection of old node connections, the farther the dependence of cluster coefficients on vertex degree of the network is from the power law form, but the closer to the uniform situation, i.e. exponential form or Poisson form.
引文
[1]Erzsébet Ravasz and Albert-LászlóBarabási.Hierarchical organization in complex networks.Phys.Rev.E 67 026112,2003.
[2]Parongama Sen,Subinay Dasgupta et al.Phys.Rev.E 67036106,2003.
[3]Anjan Kumar Chandra and Subinay Dasgupta.Physica A2005:357-436
[4]S.Battiston and M.Catanzaro.Eur.Phys.J.B 38 345(2004).
[5]Wang Ru and Cai Xu.Chin.Phys.Lett,2005.22(10):2715
[6]刘爱芬,付春花,张增平,常慧,何大韧.中国大陆电影网络的实证统计研究[J].复杂系统与复杂性科学,2007.4(3):10-16
[7]Fu C-H,Zhang Z-P,Chang H,Tao J-R,Chen Z-H,Dai Y-L,Zhang W,He D-R.A kind of collaborationcompetition networks[J].Physica A,2008.387:1411-1420
[8]Zhang P P,Chen K,He Y,Zhou T,Su B B,Jin Y,Chang H,Zhou Y-P,Sun L-C,Wang B-H,He D-R.Model and empirical study on some collaboration networks[J].Physica A,2006.360:599-616
[2]Parongama Sen,Subinay Dasgupta et al.Phys.Rev.E 67036106,2003.
[3]Anjan Kumar Chandra and Subinay Dasgupta.Physica A2005:357-436
[4]S.Battiston and M.Catanzaro.Eur.Phys.J.B 38 345(2004).
[5]Wang Ru and Cai Xu.Chin.Phys.Lett,2005.22(10):2715
[6]刘爱芬,付春花,张增平,常慧,何大韧.中国大陆电影网络的实证统计研究[J].复杂系统与复杂性科学,2007.4(3):10-16
[7]Fu C-H,Zhang Z-P,Chang H,Tao J-R,Chen Z-H,Dai Y-L,Zhang W,He D-R.A kind of collaborationcompetition networks[J].Physica A,2008.387:1411-1420
[8]Zhang P P,Chen K,He Y,Zhou T,Su B B,Jin Y,Chang H,Zhou Y-P,Sun L-C,Wang B-H,He D-R.Model and empirical study on some collaboration networks[J].Physica A,2006.360:599-616