Significance: The transition between free flow and congestions in traffic can be observed in our daily life. Although this traffic phenomenon is well studied in highways, traffic in a network scale (representing a city) is far from being understood. A fundamental unsolved question is how the global flow in a city is being integrated from local flows. Here, we identify a fundamental mechanism of traffic organization in a network scale as a percolation process, and we show how global traffic breaks down when identified bottlenecks are congested. These bottlenecks evolve with time according to traffic dynamics and are different from structural bottleneck links found by traditional network analysis. Improvement of traffic on these bottlenecks can significantly improve the global traffic.

Significance: With the same static road network, it is essentially unknown for urban traffic if traffic flows have the same spatial organization properties for different hours. Based on real-time high-resolution GPS data on the city scale, our results indicate two distinct modes characterized by different percolation critical exponents. The mode during rush hours on working days behaves like a 2D lattice with mainly short-range links, while the mode for other instants behaves like a small world (i.e., a lattice with long-range links). The difference between these two modes is explained here by the free flow on urban highways during nonrush hours, which is like adding long-range links in a 2D lattice. In contrast, during rush hours, such links almost disappear.

Social media can be a double-edged sword for society, either as a convenient channel exchanging ideas or as an unexpected conduit circulating fake news through a large population. While existing studies of fake news focus on theoretical modeling of propagation or identification methods based on machine learning, it is important to understand the realistic propagation mechanisms between theoretical models and black-box methods. Here we track large databases of fake news and real news in both, Weibo in China and Twitter in Japan from different cultures, which include their traces of re-postings. We find in both online social networks that fake news spreads distinctively from real news even at early stages of propagation, e.g. five hours after the first re-postings. Our finding demonstrates collective structural signals that help to understand the different propagation evolution of fake news and real news. Different from earlier studies, identifying the topological properties of the information propagation at early stages may offer novel features for early detection of fake news in social media.

Significance: Traffic congestion has become the most stubborn disease for the health of a city. Like the self-healing ability of a biological unit from diseases, transportation can also recover spontaneously from various disturbances. To describe this recovery, we define the resilience metric as the spatiotemporal congestion cluster, which can be used for other network systems. Based on large-scale GPS datasets, we reveal that the recovery behavior of transportation from congestion is governed by three scaling laws for all of the congestion scales. These scaling laws are found independent of microscopic details, including fluctuation of traffic demand and corresponding management. Our results of resilience scaling can help to better characterize and improve the adaptation and recovery of city traffic from various perturbations.

Different from the direct contact in epidemics spread, overload failures propagate through hidden functional dependencies. Many studies focused on the critical conditions and catastrophic consequences of cascading failures. However, to understand the network vulnerability and mitigate the cascading overload failures, the knowledge of how the failures propagate in time and space is essential but still missing. Here we study the spatio-temporal propagation behaviour of cascading overload failures analytically and numerically on spatially embedded networks. The cascading overload failures are found to spread radially from the centre of the initial failure with an approximately constant velocity. The propagation velocity decreases with increasing tolerance, and can be well predicted by our theoretical framework with one single correction for all the tolerance values. This propagation velocity is found similar in various model networks and real network structures. Our findings may help to predict the dynamics of cascading overload failures in realistic systems.

Many complex systems in the real world can be modeled as complex networks, which has captured in recent years enormous attention from researchers of diverse fields ranging from natural sciences to engineering. The extinction of species in ecosystems and the blackouts of power girds in engineering exhibit the vulnerability of complex networks, investigated by empirical data and analyzed by theoretical models. For studying the resilience of complex networks, three main factors should be focused on: the network structure, the network dynamics and the failure mechanism. In this review, we will introduce recent progress on the resilience of complex networks based on these three aspects. For the network structure, increasing evidence shows that biological and ecological networks are coupled with each other and that diverse critical infrastructures interact with each other, triggering a new research hotspot of “networks of networks” (NON), where a network is formed by interdependent or interconnected networks. The resilience of complex networks is deeply influenced by its interdependence with other networks, which can be analyzed and predicted by percolation theory. This review paper shows that the analytic framework for Energies 2015, 8 12188 NON yields novel percolation laws for n interdependent networks and also shows that the percolation theory of a single network studied extensively in physics and mathematics in the last 60 years is a specific limited case of the more general case of n interacting networks. Due to spatial constraints inherent in critical infrastructures, including the power gird, we also review the progress on the study of spatially-embedded interdependent networks, exhibiting extreme vulnerabilities compared to their non-embedded counterparts, especially in the case of localized attack. For the network dynamics, we illustrate the percolation framework and methods using an example of a real transportation system, where the analysis based on network dynamics is significantly different from the structural static analysis. For the failure mechanism, we here review recent progress on the spontaneous recovery after network collapse. These findings can help us to understand, realize and hopefully mitigate the increasing risk in the resilience of complex networks.