Covert networks are social networks that often consist of harmful users. Social Network Analysis (SNA) has played an important role in reducing criminal activities (e.g., counter terrorism) via detecting the influential users in such networks. There are various popular measures to quantify how influential or central any vertex is in a network. As expected, strategic and influential miscreants in covert networks would try to hide herself and her partners (called leaders ) from being detected via these measures by introducing new edges. show that the corresponding computational problem, called Hiding Leader, is NP-Complete for the degree and closeness centrality measures. We study the popular core centrality measure and show that the problem is NP-Complete even when the core centrality of every leader is only @math . On the contrary, we prove that the problem becomes polynomial time solvable for the degree centrality measure if the degree of every leader is bounded above by any constant. We then focus on the optimization version of the problem and show that the Hiding Leader problem admits a @math factor approximation algorithm for the degree centrality measure. We complement it by proving that one cannot hope to have any @math factor approximation algorithm for any constant @math unless there is a @math factor polynomial time algorithm for the Densest @math -Subgraph problem which would be considered a significant breakthrough.
The Internet and social media have fuelled 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 ‘node centrality’ analysis while minimizing the negative impact that this may have on his or her influence. We prove that an optimal solution to this problem is difficult to compute. Despite this hardness, we demonstrate how even a simple heuristic, whereby attention is restricted to the individual’s immediate neighbourhood, can be surprisingly effective in practice; for example, it could easily disguise Mohamed Atta’s leading position within the World Trade Center terrorist network. We also 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. Centrality measures are widely used to identify leaders of covert networks. We study how a group of such leaders can avoid being detected by such measures. More concretely, we study the hardness of choosing a set of edges that can be added to the network in order to decrease the leaders' ranking according to two fundamental centrality measures, namely degree, and closeness. We prove that this problem is NP-complete for each measure. We then study how the leaders can construct a network from scratch, designed specifically for them to hide in disguise. We identify a network structure that not only guarantees to hide the leaders to a certain extent, but also allows them to spread their influence across the network. The proliferation of network data in various application domains has raised privacy concerns for the individuals involved. Recent studies show that simply removing the identities of the nodes before publishing the graph social network data does not guarantee privacy. The structure of the graph itself, and in its basic form the degree of the nodes, can be revealing the identities of individuals. To address this issue, we study a specific graph-anonymization problem. We call a graph k-degree anonymous if for every node v, there exist at least k-1 other nodes in the graph with the same degree as v. This definition of anonymity prevents the re-identification of individuals by adversaries with a priori knowledge of the degree of certain nodes. We formally define the graph-anonymization problem that, given a graph G, asks for the k-degree anonymous graph that stems from G with the minimum number of graph-modification operations. We devise simple and efficient algorithms for solving this problem. Our algorithms are based on principles related to the realizability of degree sequences. We apply our methods to a large spectrum of synthetic and real datasets and demonstrate their efficiency and practical utility.