# Local Balance and Information Aggregation: A Method for Identifying Central Influencers in Networks
## 6 Conclusions  
This paper proposes a critical node identification algorithm based on local balance and multi-layer neighbor information aggregation (LBIA). The local balance value is introduced to propagate and aggregate information, and the improved PKs algorithm is used to encapsulate the node's individual information. These two types of information are then considered together to identify critical nodes in the network. This method addresses the issue of inaccurately identifying critical nodes in restricted regions. Furthermore, due to its low time complexity, it is suitable for large-scale networks. We evaluated the performance of LBIA by comparing it with nine other algorithms across nine different networks. The experimental results show that LBIA achieved the best accuracy in identification, with an average Kendall value of 0.7330, while the average Kendall values of other algorithms ranged from 0.3 to 0.7. LBIA significantly outperformed the other algorithms on three of the networks, which all had a larger number of restricted regions. In terms of the accuracy of identifying the top-10 nodes, LBIA's consistency ranged from 0.82 to 1. As the number of nodes increased, LBIA's Jaccard values stabilized between 0.6 and 0.8 across different networks, while the other algorithms showed instability with network changes. In terms of distinguishing capability, LBIA achieved a monotonicity value of 1, with no nodes having identical values. LBIA exhibited the best overall per  
Figure 8: Scatter Plot of correlation for different algorithms on the Soc-hamster network: the blue circles represent points with the algorithm value and the SIR value as coordinates. The red dash line represents the points that are on this line have a perfectly positive correlation property, and the further away from the line, the weaker the correlation. formance across nine networks, particularly in tightly interconnected networks, where it outperformed the other algorithms in all three metrics. This indicates that the algorithm is broadly applicable to various network types and demonstrates distinct advantages in specific network configurations. The LBIA algorithm improves on the limitations of the existing algorithms in terms of the bidirectional propagation of information and significantly reduces the problem of bias due to the repeated propagation of information during node identification by proposing the concept of the local balance value. Experimental results indicate that the algorithm exhibits superior performance across various network structures. Moreover, by only considering information from local neighborhood nodes, the LBIA algorithm not only ensures high accuracy in identification but also significantly reduces computational complexity. However, we did not consider the impact of the edge weight distribution on information propagation. As the research continues, we plan to extend LBIA to weighted and directed networks. Conceptualization, L.F.; methodology, G.M. and L.F.; software, L.F. and G.M. ; validation, G.M. ; investigation, Z.D. ; resources, L.F. and Z.D. ; writing--original draft preparation, L.F. and G.M. ; writing--review and editing, Z.D., L.F., Y.B. and X.Z. ; supervision, L.F.; funding acquisition, Z.D. All authors have read and agreed to the published version of the manuscript. This research was funded by the Key Research and Development Projects of Shaanxi Province grant number 2020 ZDLNY03-06, the Key Industry Innovation Chain of Shaanxi grant number 2021 ZDLGY02-02, Xi'an Science and Technology Plan Project grant number 23 KGDW0018-2023, Shaanxi Province Natural Science Basic Research Program Project grant number 2024 JC-YBMS-557, and the Natural Science Basis Research Plan in Shaanxi Province of China grant number 2023 JC-YB-517. Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. The authors declare no conflicts of interest.