  Networks with underlying metric spaces attract increasing research attention
in network science, statistical physics, applied mathematics, computer science,
sociology, and other fields. This attention is further amplified by the current
surge of activity in graph embedding. In the vast realm of spatial network
models, only a few reproduce even the most basic properties of real-world
networks. Here, we focus on three such properties---sparsity, small worldness,
and clustering---and identify the general subclass of spatial homogeneous and
heterogeneous network models that are sparse small worlds and that have nonzero
clustering in the thermodynamic limit. We rely on the maximum entropy approach
where network links correspond to noninteracting fermions whose energy
dependence on spatial distances determines network small worldness and
clustering.
