Sandpile on Scale-Free Networks

We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, where the threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent. Applying the theory of the multiplicative branching process, we obtain the exponent and the dynamic exponent z as a function of the degree exponent of SF networks as =/ (-1) and z= (-1) / (-2) in the range 23, with a logarithmic correction at =3. The analytic solution supports our numerical simulation results. We also consider the case of a uniform threshold, finding that the two exponents reduce to the mean-field ones.