**Abstract**

It is by now a standard practice to use the concepts and terminologies of network science to analyze social networks of interconnections between people such as Facebook, Twitter and LinkedIn. The powers and implications of such social network analysis are indeed indisputable; for example, such analysis may uncover previously unknown knowledge on community-based involvements, media usages and individual engagements. However, all these benefits are not necessarily costfree since a malicious individual could compromise privacy of users of these social networks for harmful purposes that may result in the disclosure of sensitive data that may be linked to its users. A natural way to avoid this consists of an "anonymization process" of the relevant social network. However, since such anonymization processes may not always succeed, an important research goal is to quantify and measure how much privacy a given social network can achieve. Toward this goal, some recent research works have aimed at evaluating the resistance of a social network against active privacy-violating attacks by introducing and studying a new and meaningful privacy measure for social networks. In this chapter, we review both theoretical and empirical aspects of such privacy violation measures of large networks under active attacks.

**Keywords:** social networks, privacy measure, active attacks, (*k*, ℓ)-anonymity, algorithmic complexity
