A deterministic representation of cascade spreading in complex networks

The influence of a network configuration on its vulnerability to cascade spreading is investigated. In our model, a failure cascade is initiated by sequential disturbances that impose additional loads on each node that lead to local failure. The resulting redistribution of these additional loads on neighboring nodes in turn leads to a cascade of local failures along the network connections. The extent of these failures on the network depends on the reachability of its constituent parts and on its specific link-node configuration, properties that are quantitatively characterized by a global connection efficiency and a coefficient of variability, respectively. The results show that lower values of the global efficiency make the network more resilient to cascading failures by increasing the critical failure load. Yet, once a critical load is exceeded, the transition to complete failure occurs more rapidly. The converse is true when this efficiency is lower. The analysis provides parameters that are relevant to the design of networks