  Maximal clique enumeration appears in various real-world networks, such as
social networks and protein-protein interaction networks for different
applications. For general graph inputs, the number of maximal cliques can be up
to $3^{|V|/3}$. However, many previous works suggest that the number is much
smaller than that on real-world networks, and polynomial-delay algorithms
enable us to enumerate them in a realistic-time span. To bridge the gap between
the worst case and practice, we consider the number of maximal cliques in two
popular models of real-world networks: Euclidean random geometric graphs and
hyperbolic random graphs. We show that the number of maximal cliques on
Euclidean random geometric graphs is lower and upper bounded by
$\exp(\Omega(|V|^{1/3}))$ and $\exp(O(|V|^{1/3+\epsilon}))$ with high
probability for any $\epsilon > 0$. For a hyperbolic random graph, we give the
bounds of $\exp(\Omega(|V|^{(3-\gamma)/6}))$ and
$\exp(O(|V|^{(3-\gamma+\epsilon)/6)}))$ where $\gamma$ is the power-law degree
exponent between 2 and 3.
