Stability of Dominating Sets in Complex Networks against Random and Targeted Attacks

We conduct an extensive numerical analysis of the effects of network damage on dominating sets that occur at either randomly selected nodes or at the highest-degree nodes, in synthetic scale-free and real complex networks. We focus on the fraction of nodes that remain dominated after the damage has occurred, defined as stability. We find that minimum dominating sets (MDS), despite being optimal for minimum cost influencing and information spreading, are particularly vulnerable to both types of network damage. However, suboptimal (larger) dominating sets, selected by heuristic methods, have higher stability due to increased redundancy of selected dominators. We also propose two new algorithms for finding dominating sets with freely adjustable set sizes and resulting stabilities. Given identical set sizes, the stability of our dominating sets are at least as high as those provided by MDS or heuristic methods.