Syncretic K-shell algorithm for node importance identification and invulnerability evaluation of urban rail transit network

In this paper, the Syncretic K-shell algorithm is developed and applied to identify the node importance and evaluate the invulnerability in an urban rail transit network, which is based on the idea that the nodes removed later are more important than those removed former, the nodes with the same core value also have different importance. It has a very important strategic significance for optimizing network structure, improving operational efficiency, and providing targeted protection and designated accident prevention measures for stations with different importance. Syncretic Core Value, as the node importance recognition criterion of Syncretic K-shell algorithm, considers the influence of node degree, cumulative core value and syncretic weight of adjacent nodes on node importance. Firstly, we use space L to establish the indirect and non-weighted urban rail transit network. Then, the node importance recognition steps of Syncretic K-shell algorithm are introduced. Then, a numerical study of the proposed Syncretic K-shell algorithm is conducted, and the Degree Centrality, Betweenness Centrality, Closeness Centrality, Mixed Degree Decomposition and Classical K-shell are used as comparison approaches. The node anti-destruction under node failure (including intentional attack and random attack) is evaluated, and finally, an example study is conducted with the background of Chengdu Metro Network. The results show that the important nodes identified by Syncretic K-shell have a greater impact on anti-destruction performance. The research found that Chengdu Metro Network is more vulnerable to attack and easy to be destroyed under intentional attack. Finally, two coping strategies are provided. According to the research results, we can conclude that compared with the previous node importance recognition methods, Syncretic K-shell algorithm has five advantages: (i) it can distinguish the importance between nodes with the same core value; (ii) considering the global and local centrality of nodes, the Syncretic Core Value of nodes can better reflect the importance of nodes; (iii) it can recognize the importance of nodes in networks with the same degree value or without obvious aggregation characteristics; (iv) the time complexity of Syncretic K-shell algorithm can be used for the recognition of node importance in large-scale networks; (v) it can better distinguish and amplify the differences between nodes, and quickly and effectively rank the importance of nodes.