  We study the population properties of merging binary black holes in the
second LIGO--Virgo Gravitational-Wave Transient Catalog assuming they were all
formed dynamically in gravitationally bound clusters. Using a phenomenological
population model, we infer the mass and spin distribution of first-generation
black holes, while self-consistently accounting for hierarchical mergers.
Considering a range of cluster masses, we see compelling evidence for
hierarchical mergers in clusters with escape velocities $\gtrsim
100~\mathrm{km\,s^{-1}}$. For our most probable cluster mass, we find that the
catalog contains at least one second-generation merger with $99\%$ credibility.
We find that the hierarchical model is preferred over an alternative model with
no hierarchical mergers (Bayes factor $\mathcal{B} > 1400$) and that GW190521
is favored to contain two second-generation black holes with odds
$\mathcal{O}>700$, and GW190519, GW190602, GW190620, and GW190706 are
mixed-generation binaries with $\mathcal{O} > 10$. However, our results depend
strongly on the cluster escape velocity, with more modest evidence for
hierarchical mergers when the escape velocity is $\lesssim
100~\mathrm{km\,s^{-1}}$. Assuming that all binary black holes are formed
dynamically in globular clusters with escape velocities on the order of tens of
$\mathrm{km\,s^{-1}}$, GW190519 and GW190521 are favored to include a
second-generation black hole with odds $\mathcal{O}>1$. In this case, we find
that $99\%$ of black holes from the inferred total population have masses that
are less than $49\,M_{\odot}$, and that this constraint is robust to our choice
of prior on the maximum black hole mass.
