Closure, connectivity and degree distributions: Exponential random graph (p*) models for directed social networks
Closure, connectivity and degree distributions: Exponential random graph (p*) models for directed social networks
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DOI：
10.1016/j.socnet.2008.10.006
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发表时间：
2009-05-01
期刊：
影响因子：
3.1
通讯作者：
Wang, Peng
中科院分区：
文献类型：
--
作者：
Robins, Garry;Pattison, Pip;Wang, Peng
Snijders等人[Snijders，T.A.B.，Rattison，RE.，罗宾斯公司，汉多克M.，2006.指数随机图模型的新规范。Sociological Methodology 36，99 -153]与常用的马尔可夫随机图模型相比，在模型拟合方面表现出实质性的改进。Snijders等人，然而，集中在非有向图，只有有限的扩展到有向图。特别是，他们提出了一个基于路径缩短的传递封闭参数。在本文中，我们解释了理论和经验的优势，推广到额外的封闭效应。我们提出了三个新的基于三元的参数来表示不同版本的三元封闭：循环效应;传递性的基础上共享的选择的合作伙伴;和传递性的基础上共享的流行。我们将后两种效应解释为结构同质性的形式，其中关系的出现是因为节点共享一种局部结构等价形式。我们发现，对于一些数据集，路径缩短参数是不足以实际建模，而结构同质性参数可以产生有用的模型与独特的解释。我们还介绍了相应的多个双路连接的低阶效应。我们的例子表明，在和出度分布可以更好地建模时，基于星的参数补充参数的孤立节点，源（节点与零度）和汇（节点与零度）的数量。包含一个马尔可夫混合星星参数也可以帮助模型之间的相关性在度和度。我们选择了约50个图形特征进行研究，在拟合优度诊断，涵盖了各种重要的网络属性，包括密度，互易性，测地线分布，度分布，和各种形式的封闭。作为实证说明，我们开发了两套组织网络数据模型：一个信任网络内的培训组，和一个工作困难的网络内的政府工具。(C)2008 Elsevier B. V.保留所有权利。
The new higher order specifications for exponential random graph models introduced by Snijders et al. [Snijders,T.A.B., Rattison, RE., Robins G.L., Handcock. M., 2006. New specifications for exponential random graph models. Sociological Methodology 36,99-153] exhibit substantial improvements in model fit compared with the commonly used Markov random graph models. Snijders et al., however, concentrated on non-directed graphs, with only limited extensions to directed graphs. In particular, they presented a transitive closure parameter based on path shortening. In this paper, we explain the theoretical and empirical advantages in generalizing to additional closure effects. We propose three new triadic-based parameters to represent different versions of triadic closure: cyclic effects; transitivity based on shared choices of partners; and transitivity based on shared popularity. We interpret the last two effects as forms of structural homophily, where ties emerge because nodes share a form of localized structural equivalence. We show that, for some datasets, the path shortening parameter is insufficient for practical modeling, whereas the structural homophily parameters can produce useful models with distinctive interpretations. We also introduce corresponding lower order effects for multiple two-path connectivity. We show by example that the in- and out-degree distributions may be better modeled when star-based parameters are supplemented with parameters for the number of isolated nodes, sources (nodes with zero in-degrees) and sinks (nodes with zero out-degrees). Inclusion of a Markov mixed star parameter may also help model the correlation between in- and out-degrees. We select some 50 graph features to be investigated in goodness of fit diagnostics, covering a variety of important network properties including density, reciprocity, geodesic distributions, degree distributions, and various forms of closure. As empirical illustrations, we develop models for two sets of organizational network data: a trust network within a training group, and a work difficulty network within a government instrumentality. (C) 2008 Elsevier B.V. All rights reserved.