  The study of the response of complex dynamical social, biological, or
technological networks to external perturbations has numerous applications.
Random Boolean Networks (RBNs) are commonly used a simple generic model for
certain dynamics of complex systems. Traditionally, RBNs are interconnected
randomly and without considering any spatial extension and arrangement of the
links and nodes. However, most real-world networks are spatially extended and
arranged with regular, power-law, small-world, or other non-random connections.
Here we explore the RBN network topology between extreme local connections,
random small-world, and pure random networks, and study the damage spreading
with small perturbations. We find that spatially local connections change the
scaling of the relevant component at very low connectivities ($\bar{K} \ll 1$)
and that the critical connectivity of stability $K_s$ changes compared to
random networks. At higher $\bar{K}$, this scaling remains unchanged. We also
show that the relevant component of spatially local networks scales with a
power-law as the system size N increases, but with a different exponent for
local and small-world networks. The scaling behaviors are obtained by
finite-size scaling. We further investigate the wiring cost of the networks.
  From an engineering perspective, our new findings provide the key design
trade-offs between damage spreading (robustness), the network's wiring cost,
and the network's communication characteristics.
