  A dissipative sandpile model (DSM) is constructed and studied on small world
networks (SWN). SWNs are generated adding extra links between two arbitrary
sites of a two dimensional square lattice with different shortcut densities
$\phi$. Three different regimes are identified as regular lattice (RL) for
$\phi\lesssim 2^{-12}$, SWN for $2^{-12}<\phi< 0.1$ and random network (RN) for
$\phi\ge 0.1$. In the RL regime, the sandpile dynamics is characterized by
usual Bak, Tang, Weisenfeld (BTW) type correlated scaling whereas in the RN
regime it is characterized by the mean field (MF) scaling. On SWN, both the
scaling behaviors are found to coexist. Small compact avalanches below certain
characteristic size $s_c$ are found to belong to the BTW universality class
whereas large, sparse avalanches above $s_c$ are found to belong to the MF
universality class. A scaling theory for the coexistence of two scaling forms
on SWN is developed and numerically verified. Though finite size scaling (FSS)
is not valid for DSM on RL as well as on SWN, it is found to be valid on RN for
the same model. FSS on RN is appeared to be an outcome of super diffusive sand
transport and uncorrelated toppling waves.
