# Directed Network Disassembly Method Based on Non-Backtracking Matrix
## 5 Experimental Results
\(r>0\) indicates that the entire network presents an assortative structure, and the nodes with large degrees tend to be connected to the nodes with large degrees. \(r<0\) indicates that the entire network presents  
Figure 4: Curve graph of disassembly cost and clustering coefficient of directed ER random network and directed BA random network. Figure 5: Curve graph of real network disassembly cost and clustering coefficient. disassortativity, and \(r=0\) indicates that there is no correlation in the network structure. In the experiment, the change of the network structure by the dismantling of the DIR method is analyzed by observing the influence of the dismantling process on the network assimilation index. As shown in Figures 6 and 7, the changes of the assortativity in the network of the DIR method are less in number than in the other two methods. Whether in the ER random network or in the real network, when the disassembly cost is less than 0.7, the blue curve is more gentle, the change of the global assortativity of the network is smaller, and the influence of removing the overlapping nodes between the edge modules on the assortativity of the network is smaller than that of the GND and Min-Sum methods. The module degree [28] is used as a performance index to measure the community division. It is used to see the impact on the structure of the network community when we disassemble the network. The module degree function is \(Q=\frac{1}{2}\sum_{i,j}a_{ij}\delta\big{(}c_{i},c_{j}\big{)}\), where \(a_{ij}\) is an element in the point adjacency matrix \(A\), \(c_{i}\), \(c_{j}\) is the community to which node \(i\) and \(j\) belong to, and \(\delta\big{(}c_{i},c_{j}\big{)}\) is the membership function. If \(i\) and \(j\) are in the same community, it is 1, otherwise it is 0. Figure 6: Curve graph of disassembly cost and assortative coefficient of directed ER random network and directed BA random network. Figure 2:0 Curve graph of real network disassembly cost and assortativity coefficient. The calculation of the module degree \(Q\) in the disassembly process of the DIR method is shown in Figure 2:1 It can be seen that when the disassembly cost is less than 0.8 in the picture, the module degree \(Q\) increases with the increase in the disassembly cost. It shows that the removal node in the disassembly process also deletes the inter-group edges between different communities, which plays a certain role in promoting effective community division. When the cost is greater than 0.88, the disassembly will destroy the inter-group edges within the community and cause the modularity \(Q\) to decrease sharply. In summary, the directed network disassembly (DIR) method we proposed in all the experiments has a higher disassembly efficiency than the GND and Min-Sum methods in both artificial directed networks and real directed networks. When the network is disassembled to the same scale, the DIR method incurs the lowest cost; at the same time, by comparing the clustering coefficient and the assortative coefficient in the disassembly process, it is also proved that the DIR method can reduce the influence of disassembly on the network clustering coefficient and the assortative coefficient in the disassembly process, and can also effectively retain the information in the network; the influence of the DIR method on network modularity is also explored through experiments. When the disassembly scale is less than a given threshold, the DIR method has a certain promoting effect on network community division.