Preferential network perturbation

We study network robustness to perturbation for a pair of non-directional networks, motivated by applications in cancer network modelling. The susceptibility of single networks to attack and failure has been well-studied, but a similar problem for a pair of networks with non-zero similarity has so far not been considered. In the current approach, we wish to maximise the perturbation of one network while minimising that of a second network, thus achieving a “preferential” perturbation. We focus on network pairs derived from a single underlying network which we call “correlated” networks, and use model networks to generate results and principles for general network topologies.We investigate a number of vertex ranking methods to maximise the preferential perturbation, each involving successive vertex removal, and we show that novel robustness or susceptibility metrics are required for preferential perturbation. We propose that the average perturbation gradient up to maximum perturbation is generally the most suitable metric, which accounts for both the extent of perturbation and fraction of vertices removed. Vertex betweenness is found to be the optimum vertex ranking method for a network ensemble according to this metric, which requires no knowledge of the second network. For a particular network pair, however, none of the methods studied is guaranteed to be optimum. The maximum perturbation score is an alternative susceptibility metric, which is suitable if there is no “cost” associated with vertex removal. Preferential perturbation is strongly influenced by network similarity, and we investigate other topological dependencies.