Network representation using graph root distributions
The Annals of Statistics · 2021 · Volume 49 · Issue 2
Abstract
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work, we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes are independent random vectors in a linear space equipped with an indefinite inner product, and the edge probability between two nodes equals the inner product of the corresponding node vectors. Therefore, the distribution of exchangeable random graphs in this subclass can be represented by a node sampling distribution on this linear space, which we call the graph root distribution. We study existence and identifiability of such representations, the topological relationship between the graph root distribution and the exchangeable random graph sampling distribution and estimation of graph root distributions.
Keywords
62E10, 62G05, 62M15, exchangeable random graph, Kreǐn space, network data, spectral embedding
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