# Local Balance and Information Aggregation: A Method for Identifying Central Influencers in Networks
## 2 Related Work  
The node centrality method is typically used to measure the influence of a node's relative position in a network. These algorithms provide an intuitive way to assess node importance. Degree centrality (DC) [18] determines a node's importance by directly counting the number of neighbors of the node. However, it is not able to distinguish the relative importance between nodes with the same number of neighbors. Closeness centrality (CC) measures the average distance of a node from all other nodes in the network, favoring more centrally located nodes. While this approach provides a global perspective, it also has high time complexity. Betweenness centrality (BC) [19] quantifies the frequency with which a node appears in the shortest paths between pairs of other nodes. A higher betweenness centrality value indicates that a node is more likely to serve as a crucial mediator in information flow. Similar to closeness centrality, BC also suffers from high time complexity.  
In recent years, several advanced algorithms have been proposed to identify key nodes in networks. The Local Clustering H-index (LCH) [20] incorporates neighborhood topology, node degree, and node quality, integrating local network characteristics with the clustering coefficient's influence, thereby enhancing the accuracy of key node identification. [PERSON] et al. introduced the Extended Cluster Coefficient Ranking Measure (ECRM) [21], which refines node identification by incorporating hierarchical structures and layering the network at a finer granularity. [PERSON] and [PERSON] [22] proposed a semi-local centrality measure as a trade-off between low-correlation centrality and computationally expensive metrics, significantly reducing computational complexity. [PERSON] et al. developed the Nearest Neighborhood Trust PageRank (NTPR) [23], which leverages structural attributes of both neighbors and nearest neighbors. This method defines ranking metrics based on degree ratio, node similarity, and the trust values of neighboring nodes. [PERSON] et al. extended this idea by collecting information from multiple levels of neighborhoods, introducing the Global Structural Influence (GSI) [24] method, which considers both local and global influences within the network.  
In addition to these algorithmic improvements, some researchers have combined existing algorithms with a variety of fields. [PERSON] et al. combined the k-shell algorithm with the gravitational formulation from physics, proposing an improved gravity centrality measure called KSGC [25]. This approach refines gravitational centrality by considering node positions in advance, thereby improving identification accuracy. [PERSON] et al. [26] proposed the PW algorithm, which utilizes the eigenvectors of the maximum and minimum eigenvalues of the Laplacian matrix to identify optimal nodes for optimizing the coupling range, and to control or influence the overall network behavior by 'pinning' these nodes. [PERSON] et al. proposed the IDME (Information Diffusion and Matthew Effect Aggregation) [27] method by using the Matthew effect to aggregate information from multiple neighboring layers.  
Existing algorithms typically identify critical nodes by evaluating node characteristics and network topology. The LBIA algorithm builds upon this framework by incorporating the dynamic properties of information propagation, considering both the information reception and dissemination capabilities of nodes to achieve the more accurate identification of critical nodes. This approach effectively integrates the high resolution of global algorithms with the computational efficiency inherent in local algorithms, thereby offering a more refined and efficient solution for critical node identification.