Acquaintance immunization with limited knowledge of network structure

Abstract

Optimal and efficient immunization of large networks remains a challenging task. Many theories and approaches have been suggested, however most of them require complete knowledge of the underlying network structure. Here, we study a targeted immunization strategy that incorporates the fact that there is often limited information on the network structure. Previous work has suggested `acquaintance' immunization, where rather than selecting a random individual to immunize, an individual is selected and then one of their acquaintances is immunized. Here, we generalize acquaintance immunization to the case where rather than selecting a random acquaintance, we examine the degrees of $n$ acquaintances and immunize the one with the highest degree. We develop and solve an analytic framework for this model and verify our model with extensive numerical simulations. We determine the critical percolation threshold $p_c$ and the size of the giant component, $P_\infty$, for arbitrary degree distributions. We also consider our immunization strategy on real-world networks and determine the variation of $p_c$ with increasing $n$. We find that our new approach improves on both acquaintance immunization and random immunization using limited knowledge.