  We examine a weighted-network multi-agent model with preferential selection
such that agents choose partners with the probability $p(w)$, where $w$ is the
number of their past selections. When $p(w)$ increases sublinearly with the
number of past selections ($p(w)\sim w^{\alpha}, \ \alpha<1$), agents develop a
uniform preference for all other agents. At $\alpha=1$, this state looses
stability and more complex structures form. For a superlinear increase
($\alpha>1$), strong heterogeneities emerge and agents make selections mainly
within small and sometimes asymmetric clusters. Even in a few-agent case,
formation of such clusters resembles phase transitions with spontaneous
symmetry breaking.
