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Network structure provides critical information for understanding the dynamic behavior of complex systems. However, the complete structure of real-world networks is often unavailable, thus it is crucially important to develop approaches to infer a more complete structure of networks. In this paper, we integrate the configuration model for generating random networks into an Expectation–Maximization–Aggregation (EMA) framework to reconstruct the complete structure of multiplex networks. We validate the proposed EMA framework against the Expectation–Maximization (EM) framework and random model on several real-world multiplex networks, including both covert and overt ones. It is found that the EMA framework generally achieves the best predictive accuracy compared to the EM framework and the random model. As the number of layers increases, the performance improvement of EMA over EM decreases. The inferred multiplex networks can be leveraged to inform the decision-making on monitoring covert networks as well as allocating limited resources for collecting additional information to improve reconstruction accuracy. For law enforcement agencies, the inferred complete network structure can be used to develop more effective strategies for covert network interdiction. 

Abstract Modeling the resilience of interdependent critical infrastructure (ICI) requires a careful assessment of interdependencies as these systems are becoming increasingly interconnected. The interdependent connections across ICIs are often subject to uncertainty due to the lack of relevant data. Yet, this uncertainty has not been properly characterized. This paper develops an approach to model the resilience of ICIs founded in probabilistic graphical models. The uncertainty of interdependency links between ICIs is modeled using stochastic block models (SBMs). Specifically, the approach estimates the probability of links between individual systems considered as blocks in the SBM. The proposed model employs several attributes as predictors. Two recovery strategies based on static and dynamic component importance ranking are developed and compared. The proposed approach is illustrated with a case study of the interdependent water and power networks in Shelby County, TN. Results show that the probability of interdependency links varies depending on the predictors considered in the estimation. Accounting for the uncertainty in interdependency links allows for a dynamic recovery process. A recovery strategy based on dynamically updated component importance ranking accelerates recovery, thereby improving the resilience of ICIs. 

The ability to accurately measure recovery rate of infrastructure systems and communities impacted by disasters is vital to ensure effective response and resource allocation before, during, and after a disruption. However, a challenge in quantifying such measures resides in the lack of data as community recovery information is seldom recorded. To provide accurate community recovery measures, a hierarchical Bayesian kernel model (HBKM) is developed to predict the recovery rate of communities experiencing power outages during storms. The performance of the proposed method is evaluated using cross‐validation and compared with two models, the hierarchical Bayesian regression model and the Poisson generalized linear model. A case study focusing on the recovery of communities in Shelby County, Tennessee after severe storms between 2007 and 2017 is presented to illustrate the proposed approach. The predictive accuracy of the models is evaluated using the log‐likelihood and root mean squared error. The HBKM yields on average the highest out‐of‐sample predictive accuracy. This approach can help assess the recoverability of a community when data are scarce and inform decision making in the aftermath of a disaster. An illustrative example is presented demonstrating how accurate measures of community resilience can help reduce the cost of infrastructure restoration.