Statistics and Its Interface
Volume 10 (2017)
A local structure model for network analysis
Pages: 355 – 367
The statistical analysis of networks is a popular research topic with ever widening applications. Exponential random graph models (ERGMs), which specify a model through interpretable, global network features, are common for this purpose. In this paper we introduce a new class of models for network analysis, called local structure graph models (LSGMs). In contrast to an ERGM, a LSGM specifies a network model through local features and allows for an interpretable and controllable local dependence structure. In particular, LSGMs are formulated by a set of full conditional distributions for each network edge, e.g., the probability of edge presence/absence, depending on neighborhoods of other edges. Additional model features are introduced to aid in specification and to help alleviate a common issue (occurring also with ERGMs) of model degeneracy. The proposed models are demonstrated on a network of tornadoes in Arkansas where a LSGM is shown to perform significantly better than a model without local dependence.
conditional distributions, exponential random graphs, Markov random fields, neighborhoods, network analysis
2010 Mathematics Subject Classification
Primary 05C80, 90B15. Secondary 62H11, 62P12.