## 2 Related Works
### Bridge Nodes Detection Methods
#### 2.1.1 Community-Unaware Approach  
The community-unaware approach does not rely on the community partition algorithm, but uses the local or global topology information of nodes to define the bridging of nodes. The research ideas are not limited to the definition and calculation of indicators [3; 4; 5; 6], but also including random walk-based methods [7], heuristic algorithms [8], and so on.  
Since the general definition of bridging is more based on node neighborhood, network local information is used more in the decision method of bridge nodes.  
[PERSON] et al. [3] first proposed bridging centrality in 2008 to evaluate drug targets. The definition of this indicator combines the calculation of random betweenness centrality and the bridging coefficient.  
Through this similar idea of combining global and local indicators, [PERSON] et al. [5] proposed a bridge node quantification indicator named BNC, which combines route-betweenness and the bridgeness-coefficient. For each node, its route-betweenness is the sum of routing weights through that node, and its bridgeness-coefficient is defined as the reciprocal of the sum of distances from that node to all its neighbors and indirect neighbors. Similarly, after the dispersion standardization of the above two indicators, the product is used as the final BNC score for the node.  
The community bridge finder algorithm (CBF) proposed by [PERSON] et al. [7] is a random walk-based bridge node detection algorithm, which attempts to detect bridging nodes between communities without relying on the community structure of the network. The basic idea is that the first node that is not connected back to the current random walk that has already been visited is more likely to belong to a different community. The algorithm selects a random node at the beginning and then follows a random path until a node is found not connected to multiple previously visited nodes during the random walk; then, this node is identified as a potential community bridge. It then randomly selects two of its neighbor nodes, and if neither of them is connected to a previously visited node, then the community bridge is an effective bridge.  
[PERSON] et al. [4] summarized the research results of bridge nodes in recent years in detail, and designed a neighbor-based bridge node centrality triplet NBNC to more comprehensively evaluate the bridging of nodes, which has the following form:  
\[(NG_{i}^{kcomp},NG_{i}^{ACR},|NG_{i}|) \tag{1}\]  
where \(NG_{i}^{kcomp}\) is the number of components in the neighborhood graph \(NG_{i}\) of node \(i\), \(|NG_{i}|\) is the number of nodes in \(NG_{i}\), and \(NG_{i}^{ACR}\) is the ratio of the algebraic connectivity of \(NG_{i}\) and \(|NG_{i}|\). In this paper, the neighborhood graph of a node \(i\) is defined as a graph composed of its neighbor nodes and all edges connecting the neighbor nodes, and a component is defined as a subgraph composed of nodes and edges in the graph and is not connected to the outside world. Obviously, by describing the state of the neighborhood graph after removing nodes, \(NG_{i}^{kcomp}\) intuitively defines the bridging role that nodes play in their neighborhoods. \(NG_{i}^{ACR}\) improves algebraic connectivity [9] and describes the bridging of nodes from another aspect. When using NBNC tuples to determine the bridging rank of nodes, the priority of each element is decreasing; that is, when the previous element cannot determine the bridging rank of two nodes, the next-level element index is used.  
Although the community-unaware approach eliminates the limitation of the community, it can also be directly applied to the network without community structure, but due to the limitation of the available information, it can only mine the properties related to the bridging effect from the local or global topology information of the nodes. Additionally, the goal of this type of algorithm is to find influential nodes from the perspective of bridging, and we think it is inappropriate to define bridge nodes in the community-unaware way.