Efficient network immunization under limited knowledge

Abstract

Targeted immunization or attacks of large-scale networks has attracted significant attention by the scientific community. However, in real-world scenarios, knowledge and observations of the network may be limited thereby precluding a full assessment of the optimal nodes to immunize (or remove) in order to avoid epidemic spreading such as that of current COVID-19 epidemic. Here, we study a novel immunization strategy where only n nodes are observed at a time and the most central between these n nodes is immunized (or attacked). This process is continued repeatedly until 1 − p fraction of nodes are immunized (or attacked). We develop an analytical framework for this approach and determine the critical percolation threshold pc and the size of the giant component P∞ for networks with arbitrary degree distributions P (k). In the limit of n → ∞ we recover prior work on targeted attack, whereas for n = 1 we recover the known case of random failure. Between these two extremes, we observe that as n increases, pc increases quickly towards its optimal value under targeted immunization (attack) with complete information. In particular, we find a new scaling relationship between |pc(∞) − pc(n)| and n as |pc(∞) − pc(n)| ∼ n −1 exp(−αn). For Scale-free (SF) networks, where P (k) ∼ k −γ , 2 < γ < 3, we find that pc has a transition from zero to non-zero when n increases from n = 1 to order of log N (N is the size of network). Thus, for SF networks, knowledge of order of log N nodes and immunizing them can reduce dramatically an epidemics.All rights reserved. No reuse allowed without permission.

Percolation of attack with tunable limited knowledge

“…Formally, let P (q; t) be the degree distribution of a random node in the remaining network at step t ≥ 0. Following the idea of [16], we will make use of the associated cumulative distribution F (q; t) = ∑ q s=0 P (s; t), namely, the probability that a randomly chosen remaining node at step t has degree no more than q.…”

“…for q ≥ 0. An alternative method for deriving ( 17) is also presented in [16]. We set F (−1; t) = 0 for all t as before.…”

“…For example, cyber criminals on the internet can only probe the status of some servers and routers and immunization decisionmakers during an epidemic such as COVID-19 are not able to trace social contacts of each individual in a population [15]. Liu et al [16] recently studied an attack strategy under limited knowledge, where only degrees of n nodes are observed at each time and the most connected one is removed. Under this framework, taking n as the network size recovers the traditional targeted attack and the other extremal case of n = 1 yields the random attack scenario.…”

“…Despite these advances, we still lack understanding of how incomplete knowledge of the network during an attack can affect the network robustness. Here, we develop theoretical frameworks for understanding attack strategies with limited knowledge covering not only the benefitoriented scenario in [16] but a cost-oriented model, where the least connected node among the n randomly observed nodes is removed. Attack cost has been proposed to be positively correlated with node degree in [17].…”

A Study on Drivers of Water Consumption in China From a Complex Network Perspective

“…Emphasizing the system structure and analyzing the system function from the structural perspective is the research idea of complex network theory. Many researchers have found that the function of a network depends on its structure, and the performance of individuals largely depends on their status in the network [27][28][29][30]. So far, complex network theory has been universally applied in many scientific fields such as economics [31], finance and trading [32], energy [33][34][35], climate [36][37][38].…”