2020 was an unprecedented year, with rapid and drastic changes in human mobility due to the COVID-19 pandemic. To understand the variation in commuting patterns among the Chinese population across stable and unstable periods, we used nationwide mobility data from 318 million mobile phone users in China to examine the extreme fluctuations of population movements in 2020, ranging from the Lunar New Year travel season (chunyun), to the exceptional calm of COVID-19 lockdowns, and then to the recovery periods. We observed that cross-city movements, which increased substantially in chunyun and then dropped sharply during the lockdown, are primarily dependent on travel distance and the socio-economic development of cities. Following the Lunar New Year holiday, national mobility remained low until mid-February, and COVID-19 interventions delayed more than 72.89 million people returning to large cities. Mobility network analysis revealed clusters of highly connected cities, conforming to the social-economic division of urban agglomerations in China. While the mass migration back to large cities was delayed, smaller cities connected more densely to form new clusters. During the recovery period after travel restrictions were lifted, the net flows of over 55% city pairs reversed in direction compared to before the lockdown. These findings offer the most comprehensive picture of Chinese mobility at fine resolution across various scenarios in China and are of critical importance for decision making regarding future public health emergency response, transportation planning, and regional economic development, among others.

The study of network disintegration has attracted much attention due to its wide applications, including suppressing the epidemic spreading, destabilizing terrorist network, preventing financial contagion, controlling the rumor diffusion and perturbing cancer networks. The crux of this matter is to find the critical nodes whose removal will lead to network collapse. This paper studies the disintegration of networks with incomplete link information. An effective method is proposed to find the critical nodes by the assistance of link prediction techniques. Extensive experiments in both synthetic and real networks suggest that, by using link prediction method to recover partial missing links in advance, the method can largely improve the network disintegration performance. Besides, to our surprise, we find that when the size of missing information is relatively small, our method even outperforms than the results based on complete information. We refer to this phenomenon as the "comic effect" of link prediction, which means that the network is reshaped through the addition of some links that identified by link prediction algorithms, and the reshaped network is like an exaggerated but characteristic comic of the original one, where the important parts are emphasized.Complex networks describe a wide range of systems in nature and society [1][2][3] . Examples include the Internet, metabolic networks, electric power grids, supply chains, urban road networks, and the world trade web among many others. The study of complex networks has become an important area of multidisciplinary research involving physics, mathematics, biology, social sciences, informatics, and other theoretical and applied sciences. Due to its broad applications, research on the structural robustness of complex networks, i.e., the ability to endure threats and survive accidental events, has received growing attention 4-9 and has become one of the central topics in the complex network research.In the majority of cases, networks are beneficial, such as power grids and Internet, where we want to preserve their function. Many studies have considered methods for maximizing the structural robustness of these beneficial networks [10][11][12][13][14][15][16] . In another situation by which this paper is motivated, however, we want to disintegrate a network if it is harmful, such as immunizing a population in social networks or suppressing the virus propagation in computer networks. The immunization problem is mathematically equivalent to asking how to disintegrate a given network with a minimum number of node removals 17 , which is very important since in most cases the number of immunization doses is limited or very expensive. Other examples of network disintegration include destabilizing terrorist networks 18 , preventing financial contagion 19 , controlling the rumor diffusion 20 , and perturbing cancer networks 21 . Although the problem of network disintegration attracts less attention than the problem of network protection, some related works have been de...

Robustness and small-world effect are two crucial structural features of complex networks and have attracted increasing attention. However, little is known about the relation between them. Here we demonstrate that, there is a conflicting relation between robustness and small-world effect for a given degree sequence. We suggest that the robustness-oriented optimization will weaken the small-world effect and vice versa. Then, we propose a multi-objective trade-off optimization model and develop a heuristic algorithm to obtain the optimal trade-off topology for robustness and small-world effect. We show that the optimal network topology exhibits a pronounced core-periphery structure and investigate the structural properties of the optimized networks in detail.

Many real-world systems can be described by scale-free networks with power-law degree distributions. Scale-free networks show a “robust yet fragile” feature due to their heterogeneous degree distributions. We propose to enhance the structural robustness of scale-free networks against intentional attacks by changing the displayed network structure information rather than modifying the network structure itself. We first introduce a simple mathematical model for attack information and investigate the impact of attack information on the structural robustness of scale-free networks. Both analytical and numerical results show that decreasing slightly the attack information perfection by information disturbance can dramatically enhance the structural robustness of scale-free networks. Then we propose an optimization model of disturbance strategies in which the cost constraint is considered. We analyze the optimal disturbance strategies and show an interesting but counterintuitive finding that disturbing “poor nodes” with low degrees preferentially is more effective than disturbing “rich nodes” with high degrees preferentially. We demonstrate the efficiency of our method by comparison with edge addition method and validate the feasibility of our method in two real-world critical infrastructure networks.

Dealing with the protection of critical infrastructures, many game-theoretic methods have been developed to study the strategic interactions between defenders and attackers. However, most game models ignore the interrelationship between different components within a certain system. In this paper, we propose a simultaneous-move attacker-defender game model, which is a two-player zero-sum static game with complete information. The strategies and payoffs of this game are defined on the basis of the topology structure of the infrastructure system, which is represented by a complex network. Due to the complexity of strategies, the attack and defense strategies are confined by two typical strategies, namely, targeted strategy and random strategy. The simulation results indicate that in a scale-free network, the attacker virtually always attacks randomly in the Nash equilibrium. With a small cost-sensitive parameter, representing the degree to which costs increase with the importance of a target, the defender protects the hub targets with large degrees preferentially. When the cost-sensitive parameter exceeds a threshold, the defender switches to protecting nodes randomly. Our work provides a new theoretical framework to analyze the confrontations between the attacker and the defender on critical infrastructures and deserves further study.