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Mining key nodes in complex networks has been a hotly debated topic as it played an important role in solving real-world problems.However, the existing key node mining algorithms focused on finding key nodes from a global perspective.This approach became problematic for large-scale social networks due to the unacceptable storage and computing resource overhead and the inability to utilize known query node information.A key node mining algorithm based on multiple query nodes was proposed to address the issue of key suspect mining.In this method, the known suspects were treated as query nodes, and the local topology was extracted.By calculating the critical degree of non-query nodes in the local topology, nodes with higher critical degrees were selected for recommendation.Aiming to overcome the high computational complexity of key node mining and the difficulty of effectively utilizing known query node information in existing methods, a two-stage key node mining algorithm based on multi-query was proposed to integrate the local topology information and the global node aggregation feature information of multiple query nodes.It reduced the calculation range from global to local and quantified the criticality of related nodes.Specifically, the local topology of multiple query nodes was obtained using the random walk algorithm with restart strategy.An unsupervised graph neural network model was constructed based on the graphsage model to obtain the embedding vector of nodes.The model combined the unique characteristics of nodes with the aggregation characteristics of neighbors to generate the embedding vector, providing input for similarity calculations in the algorithm framework.Finally, the criticality of nodes in the local topology was measured based on their similarity to the features of the query nodes.Experimental results demonstrated that the proposed algorithm outperformed traditional key node mining algorithms in terms of time efficiency and result effectiveness.

Mining key nodes in complex networks has been a hotly debated topic as it played an important role in solving real-world problems.However, the existing key node mining algorithms focused on finding key nodes from a global perspective.This approach became problematic for large-scale social networks due to the unacceptable storage and computing resource overhead and the inability to utilize known query node information.A key node mining algorithm based on multiple query nodes was proposed to address the issue of key suspect mining.In this method, the known suspects were treated as query nodes, and the local topology was extracted.By calculating the critical degree of non-query nodes in the local topology, nodes with higher critical degrees were selected for recommendation.Aiming to overcome the high computational complexity of key node mining and the difficulty of effectively utilizing known query node information in existing methods, a two-stage key node mining algorithm based on multi-query was proposed to integrate the local topology information and the global node aggregation feature information of multiple query nodes.It reduced the calculation range from global to local and quantified the criticality of related nodes.Specifically, the local topology of multiple query nodes was obtained using the random walk algorithm with restart strategy.An unsupervised graph neural network model was constructed based on the graphsage model to obtain the embedding vector of nodes.The model combined the unique characteristics of nodes with the aggregation characteristics of neighbors to generate the embedding vector, providing input for similarity calculations in the algorithm framework.Finally, the criticality of nodes in the local topology was measured based on their similarity to the features of the query nodes.Experimental results demonstrated that the proposed algorithm outperformed traditional key node mining algorithms in terms of time efficiency and result effectiveness.

In order to solve the problem of high time-consuming and resource-consuming quantitative calculation of large-scale industrial control network attack graphs, a key path analysis method for large-scale industrial control networks was proposed.Firstly, the idea of cut set was used to calculate the key nodes set of Bayesian attack graph by combining the atomic attack income in industrial control network, which solved the problem that the current cut set algorithm only considers the key nodes in graph structure.Secondly, a dynamic updating strategy of Bayesian attack graph which only updated the attack probability of key nodes was proposed to efficiently calculate the attack probability of the whole graph and analyze the key path of attack graph.The experimental results show that the proposed method can not only ensure the reliability of the calculation results of large-scale industrial control attack graphs, but also can significantly reduce the time consumption and have a significant improvement in the calculation efficiency.

In order to solve the problem of high time-consuming and resource-consuming quantitative calculation of large-scale industrial control network attack graphs, a key path analysis method for large-scale industrial control networks was proposed. Firstly, the idea of cut set was used to calculate the key nodes set of Bayesian attack graph by combining the atomic attack income in industrial control network, which solved the problem that the current cut set algorithm only considers the key nodes in graph structure. Secondly, a dynamic updating strategy of Bayesian attack graph which only updated the attack probability of key nodes was proposed to efficiently calculate the attack probability of the whole graph and analyze the key path of attack graph. The experimental results show that the proposed method can not only ensure the reliability of the calculation results of large-scale industrial control attack graphs, but also can significantly reduce the time consumption and have a significant improvement in the calculation efficiency.