Comparing the sensitivity of social networks, web graphs, and random graphs with respect to vertex removal

Abstract

The sensitivity of networks regarding the removal of vertices has been studied extensively within the last 15 years. A common approach to measure this sensitivity is (i) removing successively vertices by following a specific removal strategy and (ii) comparing the original and the modified network using a specific comparison method. In this paper we apply a wide range of removal strategies and comparison methods in order to study the sensitivity of medium-sized networks from real world and randomly generated networks. In the first part of our study we observe that social networks and web graphs differ in sensitivity. When removing vertices, social networks are robust, web graphs are not. This effect is conclusive with the work of Boldi et al. who analyzed very large networks. For similarly generated random graphs we find that the sensitivity highly depends on the comparison method. The choice of the removal strategy has surprisingly marginal impact on the sensitivity as long as we consider removal strategies implied by common centrality measures. However, it has a strong effect when removing the vertices in random order.