  We analyze large-scale patterns in three-dimensional turbulent convection in
a horizontally extended square convection cell by Lagrangian particle
trajectories calculated in direct numerical simulations. A simulation run at a
Prandtl number Pr $=0.7$, a Rayleigh number Ra $=10^5$, and an aspect ratio
$\Gamma=16$ is therefore considered. These large-scale structures, which are
denoted as turbulent superstructures of convection, are detected by the
spectrum of the graph Laplacian matrix. Our investigation, which follows
Hadjighasem {\it et al.}, Phys. Rev. E {\bf 93}, 063107 (2016), builds a
weighted and undirected graph from the trajectory points of Lagrangian
particles. Weights at the edges of the graph are determined by a mean dynamical
distance between different particle trajectories. It is demonstrated that the
resulting trajectory clusters, which are obtained by a subsequent $k$-means
clustering, coincide with the superstructures in the Eulerian frame of
reference. Furthermore, the characteristic times $\tau^L$ and lengths
$\lambda_U^L$ of the superstructures in the Lagrangian frame of reference agree
very well with their Eulerian counterparts, $\tau$ and $\lambda_U$,
respectively. This trajectory-based clustering is found to work for times
$t\lesssim \tau\approx\tau^L$. Longer time periods $t\gtrsim \tau^L$ require a
change of the analysis method to a density-based trajectory clustering by means
of time-averaged Lagrangian pseudo-trajectories, which is applied in this
context for the first time. A small coherent subset of the pseudo-trajectories
is obtained in this way consisting of those Lagrangian particles that are
trapped for long times in the core of the superstructure circulation rolls and
are thus not subject to ongoing turbulent dispersion.
