| Summary: | The increasing complexity and interdependency of todays networks highlight the importance of studying network robustness to failure and attacks. Many large-scale networks are prone to cascading effects where a limited number of initial failures (due to attacks, natural hazards or resource depletion) propagate through the network, ultimately leading to a global failure scenario where a substantial fraction of the network loses its functionality. This phenomena is also present
in the interdependent networks where the failure of a component in one network may lead to the failure of the supported component in another network. These cascading failure scenarios often take place in networks which are embedded in space and constrained by geometry. In this thesis, we first look at such failures in a single network modeled as a random geometric graph (RGG). We introduce and analyze a continuous cascading failure model where a node has an initial continuously-valued
state and fails if the aggregate state of its neighbors falls below a threshold. Within this model, we derive analytical conditions for the occurrence and non-occurrence of cascading node failure, respectively. Then we study the robustness of two interdependent networks under node failures. By modeling each network using an RGG, we study conditions for the percolation of two interdependent networks after inhomogeneous node failures. We derive analytical bounds on the interdependent
degree thresholds (k1; k2), such that the interdependent RGGs percolate after removing nodes in Gi that support more than kj nodes in Gj (8i; j 2 1; 2; i 6= j). We verify the bounds using numerical simulation and show that there is a tradeoff between k1 and k2 for maintaining percolation after the failures.
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