Local immunization strategy based on the scores of nodes

Optimization of targeted node set in complex networks under percolation and selection

Most of the existing methods for the robustness and targeted immunization problems can be viewed as greedy strategies, which are quite efficient but readily induce a local optimization. In this paper, starting from a percolation perspective, we develop two strategies, the relationship-related (RR) strategy and the prediction relationship (PR) strategy, to avoid a local optimum only through the investigation of interrelationships among nodes. Meanwhile, RR combines the sum rule and the product rule from explosive percolation, and PR holds the assumption that nodes with high degree are usually more important than those with low degree. In this manner our methods have a better capability to collapse or protect a network. The simulations performed on a number of networks also demonstrate their effectiveness, especially on large real-world networks where RR fragments each of them into the same size of the giant component; however, RR needs only less than 90% of the number of nodes which are necessary for the most excellent existing methods.

Analytical connection between thresholds and immunization strategies of SIS model in random networks

Devising effective strategies for hindering the propagation of viruses and protecting the population against epidemics is critical for public security and health. Despite a number of studies based on the susceptible-infected-susceptible (SIS) model devoted to this topic, we still lack a general framework to compare different immunization strategies in completely random networks. Here, we address this problem by suggesting a novel method based on heterogeneous mean-field theory for the SIS model. Our method builds the relationship between the thresholds and different immunization strategies in completely random networks. Besides, we provide an analytical argument that the targeted large-degree strategy achieves the best performance in random networks with arbitrary degree distribution. Moreover, the experimental results demonstrate the effectiveness of the proposed method in both artificial and real-world networks.

Fragmenting networks by targeting collective influencers at a mesoscopic level

A practical approach to protecting networks against epidemic processes such as spreading of infectious diseases, malware, and harmful viral information is to remove some influential nodes beforehand to fragment the network into small components. Because determining the optimal order to remove nodes is a computationally hard problem, various approximate algorithms have been proposed to efficiently fragment networks by sequential node removal. Morone and Makse proposed an algorithm employing the non-backtracking matrix of given networks, which outperforms various existing algorithms. In fact, many empirical networks have community structure, compromising the assumption of local tree-like structure on which the original algorithm is based. We develop an immunization algorithm by synergistically combining the Morone-Makse algorithm and coarse graining of the network in which we regard a community as a supernode. In this way, we aim to identify nodes that connect different communities at a reasonable computational cost. The proposed algorithm works more efficiently than the Morone-Makse and other algorithms on networks with community structure.

Immunization and Targeted Destruction of Networks using Explosive Percolation

A new method ("explosive immunization") is proposed for immunization and targeted destruction of networks. It combines the explosive percolation (EP) paradigm with the idea of maintaining a fragmented distribution of clusters. The ability of each node to block the spread of an infection (or to prevent the existence of a large cluster of connected nodes) is estimated by a score. The algorithm proceeds by first identifying low score nodes that should not be vaccinated or destroyed, analogously to the links selected in EP if they do not lead to large clusters. As in EP, this is done by selecting the worst node (weakest blocker) from a finite set of randomly chosen "candidates." Tests on several real-world and model networks suggest that the method is more efficient and faster than any existing immunization strategy. Because of the latter property it can deal with very large networks.