Improving the characterization of P-stability for applications in network privacy

Recently, we have found that the concept of P-stability has interesting applications in network privacy. In the context of Online Social Networks it may be used for obtaining a fully polynomial randomized approximation scheme for graph masking and measuring disclosure risk. Also by using the characterization for P-stable sequences from Jerrum, McKay and Sinclair (1992) it is possible to obtain optimal approximations for the problem of kk-degree anonymity. In this paper, we present results on P-stability considering the additional restriction that the degree sequence must not intersect the edges of an excluded graph XX, improving earlier results on P-stability. As a consequence we extend the P-stable classes of scale-free networks from Torra et al. (2015), obtain an optimal solution for kk-anonymity and prove that all the known conditions for P-stability are sufficient for sequences to be graphic.