  Recently there has been increased interest in fitting generative graph models
to real-world networks. In particular, Bl\"asius et al. have proposed a
framework for systematic evaluation of the expressivity of random graph models.
We extend this framework to Geometric Inhomogeneous Random Graphs (GIRGs). This
includes a family of graphs induced by non-metric distance functions which
allow capturing more complex models of partial similarity between nodes as a
basis of connection - as well as homogeneous and non-homogeneous feature
spaces. As part of the extension, we develop schemes for estimating the
multiplicative constant and the long-range parameter in the connection
probability. Moreover, we devise an algorithm for sampling
Minimum-Component-Distance GIRGs whose runtime is linear both in the number of
vertices and in the dimension of the underlying geometric space. Our results
provide evidence that GIRGs are more realistic candidates with respect to
various graph features such as closeness centrality, betweenness centrality,
local clustering coefficient, and graph effective diameter, while they face
difficulties to replicate higher variance and more extreme values of graph
statistics observed in real-world networks.
