Robustness of interdependent geometric networks under inhomogeneous failures

Complex systems such as smart cities and smart power grids rely heavily on their interdependent components. The failure of a component in one network may lead to the failure of the supported component in another network. Components which support a large number of interdependent components may be more vulnerable to attacks and failures. In this paper, we study the robustness of two interdependent networks under node failures. By modeling each network using a random geometric graph (RGG), we study conditions for the percolation of two interdependent RGGs after in-homogeneous node failures. We derive analytical bounds on the interdependent degree thresholds (k
₁
,k
₂
), such that the interdependent RGGs percolate after removing nodes in G
_i
that support more than k
_j
nodes in G
_j
(∀i, j ∈ {1, 2}, i ≠ j). We verify the bounds using numerical simulation, and show that there is a tradeoff between k
₁
and k
₂
for maintaining percolation after the failures.