  We consider coevolution of site status and link structures from two different
initial networks: a one dimensional Ising chain and a scale free network. The
dynamics is governed by a preassigned stability parameter $S$, and a rewiring
factor $\phi$, that determines whether the Ising spin at the chosen site flips
or whether the node gets rewired to another node in the system. This dynamics
has also been studied with Ising spins distributed randomly among nodes which
lie on a network with preferential attachment. We have observed the steady
state average stability and magnetisation for both kinds of systems to have an
idea about the effect of initial network topology. Although the average
stability shows almost similar behaviour, the magnetisation depends on the
initial condition we start from. Apart from the local dynamics, the global
effect on the dynamics has also been studied. These parameters show interesting
variations for different values of $S$ and $\phi$, which helps in determining
the steady-state condition for a given substrate.
