Evaluation indicators for node importance in airline networks based on weighted motif degree

YANG Wendong; CHI Yulin

doi:10.11860/j.issn.1673-0291.20230095

Abstract：Addressing the influence of weighted motif degree on the evaluation of node importance in airline networks,this study proposes an evaluation indicator for node importance in airline net-works based on degree and weighted motif degree,encompassing both comprehensive weighted three-node motif degree and comprehensive weighted four-node motif degree. Four indicators,in-cluding weighted clustering coefficient,weighted degree centrality,weighted betweenness central-ity,and weighted closeness centrality are introduced,and the effectiveness of the comprehensive weighted motif degree indicator is assessed through network robustness and node influence evalua-tion strategies.Utilizing the airline networks of six airlines as experimental data,the effectiveness and applicability of the proposed comprehensive weighted motif degree indicator are validated. Re-sults indicate that,compared to other indicators,the network efficiency and the relative size of the maximum connected subgraphs decline most rapidly when nodes in the six airline networks are at-tacked based on the node importance ranking results derived from the comprehensive weighted four-node motif degree. Moreover,using the top ten nodes ranked by importance calculated by the comprehensive weighted four-node motif degree as the initial set of infected nodes leads to the fast-est increase in the number of immune nodes in the airline networks of the six airlines. The node im-portance ranking results of the comprehensive weighted four-node motif degree closely align with those of the Susceptible-Infectious-Recovered (SIR) model when the infection rate is near the propagation threshold,especially in networks with smaller sizes and lower clustering coefficients. Based on the analysis results of network robustness and node influence evaluation strategies,the comprehensive weighted four-node motif degree proves to be more effective and accurate in assess-ing the node importance of weighted airline networks.