  We model an isothermal aggregation process of particles/atoms interacting
according to the Lennard-Jones pair potential by mapping the energy landscapes
of each cluster size $N$ onto stochastic networks, computing transition
probabilities {from} the network for an $N$-particle cluster to the one for
$N+1$, and connecting these networks into a single joint network. The
attachment rate is a control parameter. The resulting network representing the
aggregation of up to 14 particles contains {6427} vertices. It is not only
time-irreversible but also reducible. To analyze its transient dynamics, we
introduce the sequence of the expected initial and pre-attachment distributions
and compute them for a wide range of attachment rates and three values of
temperature. As a result, we find the {configurations most likely to be
observed} in the process of aggregation for each cluster size. We examine the
attachment process and conduct a structural analysis of the sets of local
energy minima for every cluster size. We show that both processes taking place
in the network, attachment and relaxation, lead to the dominance of icosahedral
packing in small (up to 14 atom) clusters.
