Among the most fundamental tools for social network analysis are centrality measures, which quantify the importance of every node in the network. This centrality analysis typically disregards the possibility that the network may have been deliberately manipulated to mislead the analysis. To solve this problem, a recent study attempted to understand how a member of a social network could rewire the connections therein to avoid being identified as a leader of that network. However, the study was based on the assumption that the network analyzer-the seeker-is oblivious to any evasion attempts by the evader. In this paper, we relax this assumption by modelling the seeker and evader as strategic players in a Bayesian Stackelberg game. In this context, we study the complexity of various optimization problems, and analyze the equilibria of the game under different assumptions, thereby drawing the first conclusions in the literature regarding which centralities the seeker should use to maximize the chances of detecting a strategic evader.

Centrality measures can rank nodes in a social network according to their importance. However, in many cases, a node may want to avoid being highly ranked by such measures, e.g., as is the case with terrorist networks. In this work, we study a confrontation between the seeker-the party analyzing a social network using centrality measures-and the evader-a node attempting to decrease its ranking according to such measures. We analyze the possible outcomes of modifying, i.e., adding or removing, a single edge by the evader, showing that even without complete knowledge about the network, the effects of the modification on the evader's ranking can often be predicted. We study the computational complexity of finding a set of modifications that reduce the evader's centrality ranking in an optimal way, proving that these decision problems are NP-complete. Moreover, we provide a 2-approximation for the degree centrality, and logarithmic approximation boundaries for the closeness and betweenness centralities. Finally, we define and investigate a Stackelberg game between the seeker and the evader, providing a Mixed Integer Linear Programming formulation of finding an equilibrium. Altogether, we provide a thorough analysis of the strategic aspects of hiding from centrality measures in social networks.