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We have defined a new type of clustering scheme preserving the connectivityof the nodes in network ignored by the conventional Migdal-Kadanoff bond movingprocess. Our new clustering scheme performs much better for correlation lengthand dynamical critical exponents in high dimensions, where the conventionalMigdal-Kadanoff bond moving scheme breaks down. In two and three dimensions wefind the dynamical critical exponents for the kinetic Ising Model to be z=2.13and z=2.09, respectively at pure Ising fixed point. These values are in verygood agreement with recent Monte Carlo results. We investigate the phasediagram and the critical behaviour for randomly bond diluted lattices in d=2and 3, in the light of this new transformation. We also provide exactcorrelation exponent and dynamical critical exponent values on hierarchicallattices with power-law degree distributions, both in the pure and randomcases.Comment: 8 figure

Dynamical real-space renormalization group calculations with a highly connected clustering scheme on disordered networks