The latent space approach to complex networks has revealed fundamental principles and symmetries, enabling geometric methods. However, the conditions under which network topology implies geometricity remain unclear. We provide a mathematical proof and empirical evidence showing that multiscale self-similarity in complex networks is a crucial factor of latent geometry. Using degree-thresholding renormalization, we prove that a general class of ensembles of random scale-free networks in Riemannian manifolds of constant curvature and of any dimension are self-similar when interactions are pairwise. Hence, both nonvanishing local clustering in the thermodynamic limit and self-similarity are required to imply geometricity. Our findings highlight that correlated links can lead to a finite clustering coefficient without self-similarity, and therefore without inherent latent geometry. The implications are significant for network mapping and ensemble equivalence between graphs and continuous spaces.

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• Clustering
• Network structure
• Patterns in complex systems
• Scaling laws of complex systems
• Network Models
• Self-similarity