I know that a small world network has two properties: small average path length (like that of a random graph) and high clustering coefficient (like that of a lattice graph). The classic model for this type of network is the Watts-Strogatz model (aka Small World Model).
However, I want to know if there are other models that can capture these properties, especially those that are not modifications of the Watts-Strogatz model.
I have tried different graph generators (i.e., network generation models) using NetworkX's Graph generators, but they returned networks with very low (<< 0.5) average clustering aside from the Watts-Strogatz model.
Some references to other small world models that I could implement with Python would be greatly appreciated. Thank you.
If you use the classic Watts-Strogatz model you're not gonna get a local clustering coefficient above 0.7.
Another model you can use the Holme-Kim model, or the modified Holme Kim model proposed in https://doi.org/10.1017/nws.2016.5 where you start with a small base network and add nodes with connections either forming triangles, or not, giving you a tuneable clustering coefficient. However this also only gets you a maximum $CC \approx 0.7$. These networks give you a degree distribution that is closer to scale-free.
You can also implement your own Watts-Strogatz type model, but have the starting network being the caveman network, or connected caveman network from networkx, which has $CC \approx 1$, and rewire from there, and with some modification you can keep a uniform degree-distribution.