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Title: The manifold hypothesis for graphs Authors:  Patrick Rubin-delanchy - University of Bristol (United Kingdom) [presenting]
Abstract: A manifold hypothesis for graphs is presented, giving several arguments. The first is empirical, showing that manifold structure appears in high-dimensional embeddings of several real-world networks, and seems to give a distorted view of a true, low-dimensional latent domain. The second is that under regularity conditions, any latent position network model is equivalent to a manifold hypothesis in inner-product space. The last is that the manifold hypothesis explains how a sparse graph can have a high triangle density. We will also suggest several ways to exploit this hypothesis within statistical procedures.