Multi-layer networks arise when more than one type of relation is observed on a common set of actors. Modeling such networks within the exponential-family random graph (ERG) framework has been previously limited to special cases and, in particular, to dependence arising from just two layers. Extensions to ERGMs are introduced to address these limitations: Conway-Maxwell-Binomial distribution to model the marginal dependence among multiple layers; a "layer logic" language to translate familiar ERGM effects to substantively meaningful interactions of observed layers; and nondegenerate triadic and degree effects. The developments are demonstrated on two previously published datasets.

中文翻译：

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多层网络的指数族随机图模型

当在一组共同的参与者上观察到不止一种类型的关系时，就会出现多层网络。在指数族随机图 (ERG) 框架内对此类网络进行建模以前仅限于特殊情况，特别是仅由两层产生的依赖性。引入了 ERGM 的扩展来解决这些限制： Conway-Maxwell-Binomial 分布来模拟多层之间的边际依赖性；一种“层逻辑”语言，用于将熟悉的 ERGM 效应转化为观察层的实质上有意义的交互；和非退化的三元和度数效应。在两个先前发布的数据集上展示了这些发展。