基于改進K?shell的復雜網絡關鍵節點識別方法

摘" 要： 在復雜網絡研究中，精確辨識網絡內的關鍵節點對于深入把握網絡的結構特性和功能機制，以及增強復雜網絡運行的穩固性和安全性具有尤為重要的作用。傳統的K?shell方法僅依據節點在網絡中的位置信息，排序結果太粗粒化，使得節點的區分度不大；僅考慮剩余度的影響，默認同層節點的外層節點數相同，這限制了評估結果的精確性和分辨力。為了解決這一問題，文中提出一種新的關鍵節點識別方法，該方法在原始K?shell算法思想之上綜合考慮了局部影響力，補充了鄰居節點和次鄰居節點對所識別節點重要性的影響。首先，通過K?shell算法確定節點全局影響力，計算每個節點的[Ks]值；其次，通過度中心性算法確定所識別節點的鄰居節點的影響力，而次鄰居節點的影響力則通過其影響系數與數量的乘積來表征；最后，通過綜合考慮鄰居節點以及次鄰居節點的作用來評估節點的局部影響力。具體而言，鄰居節點的影響力通過其度中心性來量化，次鄰居節點的影響力則由其影響系數與數量的乘積來表征。以相關性、單調性以及魯棒性為評價標準，將文中方法在6個真實網絡上進行驗證，驗證結果顯示，提出的方法與目前主流方法相比，能更高效、準確地識別復雜網絡中的關鍵節點，并具有較高的分辨率和準確性。

關鍵詞： 復雜網絡； K?shell； 度中心性； 關鍵節點識別； 鄰居節點； 節點影響力

中圖分類號： TN711?34； TP399" " " " " " " " " " 文獻標識碼： A" " " " " " " " " " "文章編號： 1004?373X（2025）07?0095?09

Complex network′s key node identification based on improved K?shell method

LI Tianyu1， TENG Guifa1， YAO Jingfa2

（1. School of Information Science and Technology， Hebei Agricultural University， Baoding 071001， China;

2. Software Engineering Department， Hebei Software Institute， Baoding 071000， China）

Abstract： In the study of complex networks， accurate identification of key nodes in the network is particularly important for deeply grasping the structural characteristics and functional mechanisms of the network， as well as enhancing the stability and security of the operation of complex networks. The traditional K?shell method is based only on the location information of the node in the network， so the sorting results are too coarse?grained， which makes the node discrimination inconspicuous. In addition， it only considers the influence of the redundancy， and the number of outer nodes of the same layer nodes is assumed to be the same， which limits the accuracy and resolution of the evaluation results. In view of the above， this paper proposes a new key node identification method. This method comprehensively considers the local influence on the basis of the idea of the original K?shell algorithm， and supplements the influence of neighbor nodes and sub?neighbor nodes on the importance of the identified nodes. Firstly， the K?shell algorithm is used to determine the global influence of the nodes and calculate the [Ks] value of each node. Secondly， the influence of the neighbor nodes of the identified nodes is determined by the degree centrality algorithm， and the influence of the sub?neighbor nodes is characterized by the products of their influence coefficients and quantities. Finally， the local influence of the nodes is evaluated by considering the role of neighbor nodes and sub?neighbor nodes comprehensively. Specifically， the influence of neighbor nodes is quantified by their degree centrality， and the influence of sub?neighbor nodes is characterized by the products of their influence coefficients and quantities. Finally， the method is verified on 6 real networks with correlation， monotonicity and robustness as evaluation criteria. The verification results show that the proposed method can identify key nodes in complex networks more efficiently and accurately and has higher resolution and accuracy in comparison with the current mainstream methods.

Keywords： complex network; K?shell; degree centrality; key node identification; neighbor node; node influence

0" 引" 言

隨著復雜網絡理論研究的興起，關鍵節點識別逐漸成為該領域的熱點問題，日益受到來自社會網絡[1]、生物網絡[2]、計算機網絡[3]、管理學[4]和經濟學[5]等領域研究人員的廣泛關注?！?br>