  A two state sandpile model with preferential sand distribution is developed
and studied numerically on scale free networks with power-law degree ($k$)
distribution, {\em i.e.}: $P_k\sim k^{-\alpha}$. In this model, upon toppling
of a critical node sand grains are given one to each of the neighbouring nodes
with highest and lowest degrees instead of two randomly selected neighbouring
nodes as in a stochastic sandpile model. The critical behaviour of the model is
determined by characterizing various avalanche properties at the steady state
varying the network structure from scale free to random, tuning $\alpha$ from
$2$ to $5$. The model exhibits mean field scaling on the random networks,
$\alpha>4$. However, in the scale free regime, $2<\alpha<4$, the scaling
behaviour of the model not only deviates from the mean-field scaling but also
the exponents describing the scaling behaviour are found to decrease
continuously as $\alpha$ decreases. In this regime, the critical exponents of
the present model are found to be different from those of the two state
stochastic sandpile model on similar networks. The preferential sand
distribution thus has non-trivial effects on the sandpile dynamics which leads
the model to a new universality class.

Statistical Mechanics