  Geometric scale-free random graphs are popular models for networks that
exhibit as heavy-tailed degree distributions, small-worldness and high
clustering. In these models, vertices have weights that cause the heavy-tailed
degrees and are embedded in a metric space so that close-by groups of vertices
tend to cluster. The interplay between the vertex weights and positions heavily
affects the local structure of the random graph, in particular the occurrence
of subgraph patterns, but the dependencies in these structures and weights make
them difficult to analyze. In this paper we investigate subgraph counts using a
\textit{divide et impera} strategy: first counting the number of subgraphs in
specific classes of vertices; then computing which class yields maximum
contribution. Interestingly, the scaling behavior of induced and general
subgraphs in such geometric heavy-tailed random graphs is closely related to
the solution of a mixed-integer linear program which also shows that subgraphs
appear predominantly on vertices with some prescribed degrees and
inter-distances. Finally, we derive precise asymptotics for trees and
Hamiltonian subgraphs.
