Robustness of complex networks: Theory and application

Failures of networks, such as power outages in power systems, congestions in
transportation networks, paralyse our daily life and introduce a tremendous cascading effect on our society. Networks should be constructed and operated in a robust way against random failures or deliberate attacks.
We study how to add a single link into an existing network such that the robustness of the network is maximally improved among all the possibilities. A graph metric, the effective graph resistance, is employed to quantify the robustness of the network. Though exhaustive search guarantees the optimal solution, the computational complexity is high and is not scalable with the increase of network size. We propose strategies that take into account the structural and spectral properties of networks and indicate links whose addition result in a high robustness level.