The subject of network geometry (Boguna et al., Network Geometry, Nature Reviews Physics 2021) looks at "geometric aspects" of complex networks.

This is about studying a metric on the nodes, though can involve diffusion geometry, and fractal geometry as well.

Can one work with an "Erlangen program" for a complex network? Though each node is not the same given the high heterogeneity of the network (they are not in a "homogeneous space"), there is some "statistical symmetry", given the complex networks can be naturally embedded in hyperbolic space (D. Krioukov, Clustering Implies Geometry in Networks, Phys. Rev. Lett. 2016).

I am basically trying to understand if network geometry, in this sense, can be thought of in terms of group theory and projective geometry.