  The topology of the network of load transmitting connections plays an
essential role in the cascading failure dynamics of complex systems driven by
the redistribution of load after local breakdown events. In particular, as the
network structure is gradually tuned from regular to completely random a
transition occurs from the localized to mean field behavior of failure
spreading. Based on finite size scaling in the fiber bundle model of failure
phenomena, here we demonstrate that outside the localized regime, the load
bearing capacity and damage tolerance on the macro-scale, and the statistics of
clusters of failed nodes on the micro-scale obey scaling laws with exponents
which depend on the topology of the load transmission network and on the degree
of disorder of the strength of nodes. Most notably, we show that the spatial
structure of damage governs the emergence of the localized to mean field
transition: as the network gets gradually randomized failed clusters formed on
locally regular patches merge through long range links generating a percolation
like transition which reduces the load concentration on the network. The
results may help to design network structures with an improved robustness
against cascading failure.
