  The effect of initial spin configurations on zero-temperature Glauber spin
dynamics in complex networks is investigated. In a system in which the initial
spins are defined by centrality measures at the vertices of a network, a
variety of non-trivial diffusive behaviors arise, particularly in relation to
functional relationships between the initial and final fractions of positive
spins, some of which exhibit a critical point. Notably, the majority spin in
the initial state is not always dominant in the final state, and the phenomena
that occur as a result of the dynamics differ according on the initial
condition, even for the same network. It is thus concluded that the initial
condition of a complex network exerts an influence on spin dynamics that is
equally as strong as that exerted by the network structure.
