Hyperbolic random graphs have become a popular random graph model over the last decade, as they resemble many real-world graphs.
In particular, they have a heterogeneous degree distribution, high clustering and a small-world property.
Another property of graphs that distinguishes technical and biological from social networks is degree assortativity – a measure
that describes the correlation between degrees of adjacent nodes.
Most technical and biological graphs are found to have a significant negative assortativity, while the assortativity of social
networks is usually positive. However, hyperbolic random graphs offer no way to control the degree assortativity.
We explore and compare multiple ways to extend hyperbolic random graphs or the similar geometric inhomogeneous random graphs
so that the expected assortativity can be controlled while maintaining the properties that made hyperbolic random graphs attractive
in the first place. In particular, we describe a model with controllable assortativity that has high clustering, small-world and a
heterogeneous degree distribution. We also describe how such graphs can be generated efficiently.