## 4 Discussion  
In this paper, we fused simple distance correlation and network topological centrality into a structural inference algorithm for GRNs and tested its performance. We selected simulated and real data sets commonly used in gene regulatory network construction algorithms and compared them with existing mutual information-based and distance-correlation-based algorithms. The algorithm can better control the introduction of redundant relationships by ranking the network topological centrality and selecting the maximum distance correlation as the regulatory gene. Therefore, it is conducive to the extension of large-scale network applications, but with many nodes in large-scale networks, there may be more genes with the same node importance when measuring node importance, which may require consideration of higher-order neighbourhood information to measure node importance. As the number of genes increases, it can also lead to inaccuracies and difficulties when inferring the network.  
Node centrality is an important metric to characterise the criticality of a node. Many node importance metrics have been proposed, including degree centrality, median centrality, proximity centrality, and eigenvector centrality. The degree centrality is the simplest metric to characterise the importance of a node. [PERSON] et al. found that in scale-free or exponential networks, there are only a small number of nodes of large degree, and this are of high importance [33]. Median centrality and proximity centrality are good measures of the importance of nodes in terms of network connectivity, but are computationally complex due to the need to know global information about the network in advance, and are not suitable for large and complex networks. [PERSON] et al. investigated the extent to which different centrality measures (degree, strength, tightness, mediation, and eigenvectors) recover potential causal interactions in directed acyclic graphs [34; 35], whereas feature vector centrality shows powerful effects in measuring the importance of nodes. In summary, the algorithm in the paper has some limitations. In the next study, we will try to reconstruct  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Method** & **TP** & **FP** & **TN** & **FN** & **TPR** & **FPR** & **PPV** & **ACC** & **MCC** \\ \hline \hline CLR & 12 & 5 & 7 & 12 & 0.500 & 0.417 & 0.706 & 0.528 & 0.079 \\ ARACNE & 7 & 3 & 9 & 17 & 0.292 & 0.250 & 0.700 & 0.444 & 0.044 \\ MRNET & 17 & 6 & 6 & 7 & 0.708 & 0.500 & 0.739 & 0.639 & 0.205 \\ REL-DC & 6 & 3 & 9 & 18 & 0.250 & 0.250 & 0.667 & 0.417 & 0 \\ MRNET- & 12 & 9 & 3 & 12 & 0.500 & 0.750 & 0.572 & 0.417 & \(-\)0.239 \\ LDCNET & 6 & 1 & 11 & 18 & 0.250 & 0.083 & 0.857 & 0.472 & 0.199 \\ DCNTC & **6** & **2** & **10** & **18** & **0.25** & **0.167** & **0.75** & **0.444** & **0.095** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of different methods on the SOS DNA repair network.  
the gene regulatory network using different approaches to compute the centrality of the network topology.  
The DCNTC algorithm has a clear advantage over the distance-based REL algorithm and the distance-based MRNET algorithm in every performance indicator. The algorithm is similar to the LDCNET algorithm in that both have a central network node location. In combination with the distance-dependent initial network redundancy and network topology centrality, the DCNTC algorithm can predict the structure of the GRN more accurately.