  Self-organization to ferromagnetic phase transition in cellular automata of
spins governed by stochastic majority rule and when topology between spins is
changed, is investigated numerically. Three types of edge rewiring are
considered. The algorithm of Watts and Strogatz is applied at each time step to
establish a network evolving stochastically (the first network). The preference
functions are defined to amplify the role of strongly connected vertices (the
second network). Demand to preserve graph connectivity provides the third way
of edge rewiring. Each of these processes yields the different network:
small-world, scattered nodes with one strongly connected component, and
scale-free network when rewiring is properly adjusted. The stochastic majority
rule applied to these networks can lead or not to ferromagnetic transition.
Classical mean-field transition in case of the first and third network is
observed. Scale-free ferromagnetic transition can be observed when rewiring is
properly adjusted.
