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Abstract:
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In a latent space (LS) network model, nodes have locations in some "latent" or "social" space. The closer two nodes are in this space, the more likely they are to form an edge. Most recent work in LS modeling assumes a LS with constant curvature, which requires the space to be Euclidean, spherical, or hyperbolic. Recently, some papers have proposed using non-constant curvature spaces to represent relationships between nodes. We propose several ways to test whether a network drawn from an unknown LS has constant curvature. One idea uses properties of geodesic triangles on the space, and a second uses the idea of network Ollivier-Ricci curvature. Our approach extends to cases where only distances are observed, such as multi-dimensional scaling problems. We also discuss whether it is possible to construct such a test using only partial network data, such as Aggregated Relational Data. We discuss (1) when this test can detect deviations from constant curvature and (2) how to leverage network curvature to design efficient network seeding methods. We explore the performance of our approach with simulations and then apply our approach to several datasets.
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