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In this paper, we present the dynamics of disaster spreading from key nodes in complex networks. The key nodes have maximum and minimum out-degree nodes, which show important in spreading disaster. This paper considers directed Erdös–Rényi, scale-free and small-world networks. Using the model considering the common characteristics of infrastructure and lifeline networks, i.e., self-healing function and disaster spreading mechanism, we carry out simulations for the effects of the recovery time parameter and the time delay on the recovery rate and the number of damaged nodes. Simulation results show some typical disaster spreading characteristics, e.g., a non-equilibrium phase transition in the parameter space, disturbance from the maximum out-degree nodes resulting in more damaged effect, etc.

The misinformation spreading in social networks causes unpredictable damage to the networked system, thus inferring the misinformation source is an important research topic in the field of network science and security. Many source inference algorithms have been proposed to find the most likely propagation source through observable snapshot. However, under limited observable conditions, observing different nodes states markedly affects the algorithm’s effectiveness. Yet, we still lack relevant research on which nodes can more accurately assist us in completing source inference. Here, we propose the heuristic message-passing-based algorithm to find the key nodes that can maximize the accuracy of source inference, which uses the average rank of the source in the message-passing method as a measure and performs continuous annealing on this basis to update the set. As a comparison, we propose random selection algorithm as the basic, high-eigenvalue algorithm and high-degree algorithm focused on centrality, and basic message-passing-based algorithm from the perspective of energy entropy in message passing. Through extensive numerical simulation on artificial and real-world networks, compared with other four algorithms, our heuristic message-passing-based algorithm finds the optimal key node set that can more accurately complete source inference. Moreover, it has over 8% higher inference accuracy than other methods in low visibility situations especially.

How to identify key nodes is a challenging and significant research issue in complex networks. Some existing evaluation indicators of node importance have the disadvantages of limited application scope and one-sided evaluation results. This paper takes advantage of multiple centrality measures comprehensively, by regarding the identification of key nodes as a multi-attribute decision making (MADM) problem. Firstly, a new local centrality (NLC) measure is put forward through considering multi-layer neighbor nodes and clustering coefficients. Secondly, combining the grey relational analysis (GRA) method and the susceptible-infectious-recovered (SIR) model, a modified dynamic weighted technique for order preference by similarity to ideal solution (TOPSIS) method is proposed. Finally, the effectiveness of the NLC is illustrated by applications to nine actual networks. Furthermore, the experimental results on four actual networks demonstrate that the proposed method can identify key nodes more accurately than the existing weighted TOPSIS method.

The risk analysis of key nodes is the foundation and important link to ensure the safety of the sea lanes. To analyze the risk and provide a basis for safety management, this paper proposes a risk assessment model based on a multi-state fuzzy Bayesian network. Firstly, a fault tree model is built for risk events, revealing the causal relationships between the risk events and the influential factors. Secondly, the multiple fault state of nodes is described by fuzzy numbers. The multi-state fuzzy conditional probability table is applied to describe the uncertain logical relationship between nodes. An expert investigation method based on a confidence index is proposed to establish a multi-state, conditional probability interval table that describes the logical relationship between variables. Finally, the model parameters are determined by obtaining the exact values of the conditional probability interval table using the α-weighted valuation method for defuzzification. The risk probability distribution based on prior knowledge and known evidence is calculated. The key risk factors are then identified. Taking the risk analysis for key nodes of sea lanes as an example, the application results demonstrated the feasibility and efficiency of the proposed method.