Xiaosong Chen

Resilience of networks with community structure behaves as if under an external field

Significance Much work has focused on phase transitions in complex networks in which the system transitions from a resilient to a failed state. Furthermore, many of these networks have a community structure, whose effects on resilience have not yet been fully understood. Here, we show that the community structure can significantly affect the resilience of the system in that it removes the phase transition present in a single module, and the network remains resilient at this transition. In particular, we show that the effect of increasing interconnections is analogous to increasing external magnetic field in spin systems. Our findings provide insight into the resilience of many modular complex systems and clarify the important effects that community structure has on network resilience. Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic– paramagnetic spin system. We also study universality class by defining the analogous critical exponents δ and γ, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.

Structural resilience of spatial networks with inter-links behaving as an external field

Many real systems such as, roads, shipping routes, and infrastructure systems can be modeled based on spatially embedded networks. The inter-links between two distant spatial networks, such as those formed by transcontinental airline flights, play a crucial role in optimizing communication and transportation over such long distances. Still, little is known about how inter-links affect the structural resilience of such systems. Here, we develop a framework to study the structural resilience of interlinked spatially embedded networks based on percolation theory. We find that the inter-links can be regarded as an external field near the percolation phase transition, analogous to a magnetic field in a ferromagnetic–paramagnetic spin system. By defining the analogous critical exponents δ and γ, we find that their values for various inter-links structures follow Widoms scaling relations. Furthermore, we study the optimal robustness of our model and compare it with the analysis of real-world networks. The framework presented here not only facilitates the understanding of phase transitions with external fields in complex networks but also provides insight into optimizing real-world infrastructure networks.

Correlation and scaling behaviors of fine particulate matter (PM2.5) concentration in China

Air pollution has become a major issue and caused widespread environmental and health problems. Aerosols or particulate matters are an important component of the atmosphere and can transport under complex meteorological conditions. Based on the data of PM 2.5 observations, we develop a network approach to study and quantify their spreading and diffusion patterns. We calculate cross-correlation functions of the time lag between sites within different seasons. The probability distribution of correlation changes with season. It is found that the probability distributions in four seasons can be scaled into one scaling function with averages and standard deviations of correlation. This seasonal scaling behavior indicates that there is the same mechanism behind correlations of PM 2.5 concentration in different seasons. Further, the weighted degrees reveal the strongest correlations of PM 2.5 concentration in winter and in the North China Plain for the positive correlation pattern that is mainly caused by the transport of PM 2.5. These directional degrees show net influences of PM 2.5 along Gobi and inner Mongolia, the North China Plain, Central China, and Yangtze River Delta. The negative correlation pattern could be related to the large-scale atmospheric waves.