39 research outputs found
Hiding in Multilayer Networks
Multilayer networks allow for modeling complex relationships, where
individuals are embedded in multiple social networks at the same time. Given
the ubiquity of such relationships, these networks have been increasingly
gaining attention in the literature. This paper presents the first analysis of
the robustness of centrality measures against strategic manipulation in
multilayer networks. More specifically, we consider an "evader" who
strategically chooses which connections to form in a multilayer network in
order to obtain a low centrality-based ranking-thereby reducing the chance of
being highlighted as a key figure in the network-while ensuring that she
remains connected to a certain group of people. We prove that determining an
optimal way to "hide" is NP-complete and hard to approximate for most
centrality measures considered in our study. Moreover, we empirically evaluate
a number of heuristics that the evader can use. Our results suggest that the
centrality measures that are functions of the entire network topology are more
robust to such a strategic evader than their counterparts which consider each
layer separately.Comment: 24 pages, 10 figure
Efficient computation of the Shapley value for game-theoretic network centrality
The Shapley valueāprobably the most important normative payoff division scheme in coalitional gamesāhas 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. Fo