分类:An introduction to exponential random graph (p*) models for social networks

来自Big Physics
跳转至: 导航搜索


Garry Robins, Pip Pattison, Yuval Kalish, Dean Lusher, An introduction to exponential random graph (p*) models for social networks, Social Networks, 29(2), 173-191(2007).

Abstract

This article provides an introductory summary to the formulation and application of exponential random graph models for social networks. The possible ties among nodes of a network are regarded as random variables, and assumptions about dependencies among these random tie variables determine the general form of the exponential random graph model for the network. Examples of different dependence assumptions and their associated models are given, including Bernoulli, dyad-independent and Markov random graph models. The incorporation of actor attributes in social selection models is also reviewed. Newer, more complex dependence assumptions are briefly outlined. Estimation procedures are discussed, including new methods for Monte Carlo maximum likelihood estimation. We foreshadow the discussion taken up in other papers in this special edition: that the homogeneous Markov random graph models of Frank and Strauss [Frank, O., Strauss, D., 1986. Markov graphs. Journal of the American Statistical Association 81, 832–842] are not appropriate for many observed networks, whereas the new model specifications of Snijders et al. [Snijders, T.A.B., Pattison, P., Robins, G.L., Handock, M. New specifications for exponential random graph models. Sociological Methodology, in press] offer substantial improvement.

总结和评论

文章[1]介绍了exponential random graph models,指数分布随机图模型的概念,用来解决哪些问题。文章[2]介绍了最新进展以及参数估计的方法和工具包。文章[3]提供了一个计算的例子。 文章[4]把指数随机图模型发展到了多层次网络上。这里的多层次网络可以看做是多层网络的一种:例如上一个层次看作是下一个层次的集团结构的标记。文章[5]把模型拓展到能够加上顶点的属性,而不仅仅是网络结构。[6]给了一个用统计物理学语言做的指数随机图模型的描述,非常好。

在一般随机样本的统计性质的研究中,我们获得了统计量之后,一般要做一个统计量的显著性,或者是统计量的方差的估计,或者是把这个统计量和某个大样本的均值和方差来比较。一个实现这个显著性分析或者方差估计的方法就是Bootstrap方法。通过重抽样来产生样本,然后计算这些新样本的同一个统计量,来看实际观测到的数据的统计量的显著性[7]

在网络科学的研究中,我们可以从网路数据得到统计量。我们也需要给这样的统计量一个显著性描述,或者说方差,或者说大样本当背景来比较。

为了解决这个问题,人们提出来了零模型[8][9] ,以及这个指数随机图模型。

零模型的意思就是通过Bootstrap来产生样本。而指数随机图模型就是在所有的网络(例如顶点数量相同)中,给出来每一个网络的几率,然后通过这个几率再来计算同一个统计量的大样本的均值和方差。同时,在指数随机图模型中,这个几率的生成也是基于观测到的网络的。因此,这就有了某种更加适合这个网络的保持某种属性的随机样本。

可以考虑把指数随机图模型和网络零模型相结合,来分析网络统计量的统计显著性,在某种随机意义下的大样本对比看来。

参考文献

  1. Garry Robins, Pip Pattison, Yuval Kalish, Dean Lusher, An introduction to exponential random graph (p*) models for social networks, Social Networks, 29(2), 173-191(2007). https://doi.org/10.1016/j.socnet.2006.08.002
  2. Garry Robins, Tom Snijders, Peng Wang, Mark Handcock, Philippa Pattison Recent developments in exponential random graph (p*) models for social networks, Social Networks, Volume 29, 192-215(2007). https://doi.org/10.1016/j.socnet.2006.08.003
  3. Steven M.Goodreau, Advances in exponential random graph (p*) models applied to a large social network, Social Networks, 29, 231-248(2007). https://doi.org/10.1016/j.socnet.2006.08.001
  4. Peng Wang, Garry Robins, Philippa Pattison, Emmanuel Lazega, Exponential random graph models for multilevel networks, Social Networks, 35, 96-115(2013). https://doi.org/10.1016/j.socnet.2013.01.004
  5. M.A.J. Van Duijn, T.A.B. Snijders, B.J.H. Zijlstra, p2: a random effects model with covariates for directed graphs, Statistica Neerlandica, 58 (2004), pp. 234-254. https://onlinelibrary.wiley.com/doi/abs/10.1046/j.0039-0402.2003.00258.x
  6. Agata Fronczak, Exponential random graph models, Chapter in Encyclopedia of Social Network Analysis and Mining, R. Alhajj, J. Rokne (Eds.), Springer-Verlag, 2014, https://arxiv.org/abs/1210.7828
  7. 吴金闪,《系统科学导引》,科学出版社,http://www.systemsci.org/jinshanw/books/
  8. Sergei Maslov, Kim Sneppen, Specificity and Stability in Topology of Protein Networks, Science, 296, 910-913(2002). https://doi.org/10.1126/science.1065103
  9. 尚可可, 许小可, 基于置乱算法的复杂网络零模型构造及其应用, 电子科技大学学报, 43, 7-20(2014) https://doi.org/10.3969/j.issn.1001-0548.2014.01.002

本分类目前不含有任何页面或媒体文件。