The Internet and social media have fueled enormous interest in social network analysis. New tools continue to be developed and used to analyse our personal connections, with particular emphasis on detecting communities or identifying key individuals in a social network. This raises privacy concerns that are likely to exacerbate in the future. With this in mind, we ask the question: Can individuals or groups actively manage their connections to evade social network analysis tools? By addressing this question, the general public may better protect their privacy, oppressed activist groups may better conceal their existence, and security agencies may better understand how terrorists escape detection. We first study how an individual can evade "network centrality" analysis without compromising his or her influence within the network. We prove that an optimal solution to this problem is hard to compute. Despite this hardness, we demonstrate that even a simple heuristic, whereby attention is restricted to the individual's immediate neighbourhood, can be surprisingly effective in practice. For instance, it could disguise Mohamed Atta's leading position within the WTC terrorist network, and that is by rewiring a strikingly-small number of connections. Next, we study how a community can increase the likelihood of being overlooked by community-detection algorithms. We propose a measure of concealment, expressing how well a community is hidden, and use it to demonstrate the effectiveness of a simple heuristic, whereby members of the community either "unfriend" certain other members, or "befriend" some non-members, in a coordinated effort to camouflage their community.

Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition structure generation problem [5]. Inspired by this observation, we develop in this paper an algorithm to solve the coalition structure generation problem on graphs, where the goal is to identifying an optimal partition of a graph into connected subgraphs. More specifically, we develop a new depth-first search algorithm, and combine it with an existing dynamic programming algorithm due to Vinyals et al. [10]. The resulting hybrid algorithm is empirically shown to significantly outperform both its constituent parts when the subset-evaluation function happens to have certain intuitive properties.

The Shapley value-probably the most important normative payoff division scheme in coalitional games-has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. For instance, in the case of unweighted networks our algorithms are able to return the exact solution about 1600 times faster than the Monte Carlo approximation, even if we allow for a generous 10% error margin for the latter method.