# Directed Network Disassembly Method Based on Non-Backtracking Matrix
## 5 Experimental Results
Figure 2: Curve graph of the disassembly cost and disassembly scale of directed ER random network and directed BA random network. The clustering coefficient in graph theory is used to measure the degree of node aggregation. There is evidence that in most real-world networks, especially in social networks, nodes tend to create relatively tightly connected groups; this possibility is often greater than the average probability of randomly establishing a relationship between two nodes. A network such as \(\mathbf{G=(V,E)}\) is formally composed of a set of nodes and edges between nodes, with edges connecting nodes. The neighborhood \(N_{i}\) of a node \(v_{i}\) is defined as its adjacent node, \(N_{i}=\left\{v_{j}:e_{ij}\in E\lor e_{ji}\in E\right\}\). The local clustering coefficient \(C_{i}\) of a node in a directed network is  
\[C_{i}=\frac{\left|\left\{e_{jk}:v_{j},v_{k}\in N_{i},e_{jk}\in E\right\} \right|}{k_{i}(k_{i}-1)} \tag{8}\]  
As an alternative to the global clustering coefficient, [PERSON] and [PERSON] [19] use the average of local clustering coefficients of all vertices as the overall clustering level of the network. \[C=\frac{1}{n}\sum_{i}C_{i} \tag{9}\]  
Here, we compare the influence of the DIR and the other two disassembly methods on the degrees of node connection in the network by observing the change of the global clustering coefficient of the network during the disassembly process, and then explore the impact on the network structure. The experiment first disassembles the artificial ER random network and the BA network; the relationship between the disassembly cost and the clustering coefficient is shown in Figure 4. When the disassembly cost is less than 0.7 in the artificial ER random network, the curve of the average clustering coefficient corresponding to the DIR method is more stable than the curve of the GND and Min-Sum method, and it also reaches a stable state first in the BA network. The DIR method has less disturbances for the clustering coefficient of the whole network compared to the GND and Min-Sum method, which reflects the superiority of removing overlapping nodes between modules by dividing the edge modules. The influence of the DIR method on the network structure is smaller than that of directly deleting nodes in the network; in the ER random network, the three methods will increase the network clustering coefficient with the disassembly in a certain period of time. This is because the disassembly has caused an increasing number of nodes in the network to appear in clusters. The result of the experiment in the real network is shown in Figure 5. It can be seen that in the real-world directed network, with the increase in the disassembly cost, the three disassembly methods will reduce the clustering coefficient in the network,  
Figure 3: Curve graph of directed real network disassembly cost and disassembly scale. which is related to the sparsity of the real network. The dismantling of the nodes of the real network will reduce the agglomeration between nodes and the connection between groups will become sparse; however, it can still be seen from the graph that the curve corresponding to the DIR method is more gentle than the GND and Min-Sum methods. The influence of this aggregation phenomenon on the real network during the disassembly process is smaller than that of the two methods; and relatively speaking, the Min-Sum method will have a more obvious impact on the aggregation phenomenon of the network, because the Min-Sum method tends to remove nodes with large degrees in the network and is less able to protect the structural information of the network. The coefficient of assortativity is used to measure whether the network is assortative or disassortative. It is used to investigate whether the nodes with similar values of degree in the network tend to be connected to its approximate nodes. It can be characterized by the Pearson coefficient \(r\) (degree-degree correlation).