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Geometry can be used to explain many properties commonly observed in realnetworks. It is therefore often assumed that real networks, especially thosewith high average local clustering, live in an underlying hidden geometricspace. However, it has been shown that finite size effects can also inducesubstantial clustering, even when the coupling to this space is weak or nonexistent. In this paper, we study the weakly geometric regime, where clusteringis absent in the thermodynamic limit but present in finite systems. ExtendingMercator, a network embedding tool based on the Popularity$\times$Similarity$\mathbb{S}^1$/$\mathbb{H}^2$ static geometric network model, we show that,even when the coupling to the geometric space is weak, geometric informationcan be recovered from the connectivity alone. The fact that several realnetworks are best described in this quasi-geometric regime suggests that thetransition between non-geometric and geometric networks is not a sharp one.

Random graphs and real networks with weak geometric coupling