  We have defined a new type of clustering scheme preserving the connectivity
of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving
process. Our new clustering scheme performs much better for correlation length
and dynamical critical exponents in high dimensions, where the conventional
Migdal-Kadanoff bond moving scheme breaks down. In two and three dimensions we
find the dynamical critical exponents for the kinetic Ising Model to be z=2.13
and z=2.09, respectively at pure Ising fixed point. These values are in very
good agreement with recent Monte Carlo results. We investigate the phase
diagram and the critical behaviour for randomly bond diluted lattices in d=2
and 3, in the light of this new transformation. We also provide exact
correlation exponent and dynamical critical exponent values on hierarchical
lattices with power-law degree distributions, both in the pure and random
cases.
