## 5 Results
### Clustering Effect  
The experimental results are shown in scenarios 1, 2, and 3. In each scenario, the results of the first round of clustering of LEACH, K-LEACH, and DCK-LEACH algorithms are shown in Figure 3, which verifies the efficiency of the proposed method. The clustering effects of IEECHS-WSN and RCH-LEACH are similar to LEACH. Due to space limitations, they are not listed here. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Simulation Environment & Pychar2022.2 \\ System Properties & Intel Core i5 CPU and 16 GB of RAM \\ Area & 100 m \(\times\) 100 m \\ Number of nodes & 100, 200, 300 \\ Base station’s coordinates & (50, 150) \\ Data packet size & 4000 bit \\ Broadcast packet size & 100 bit \\ Node’s initial energy \(E_{0}\) & 0.2 J \\ \(E_{dec}\) & 50 nJ/bit \\ \(E_{da}\) & 50 nJ/bit \\ \(\varepsilon_{fs}\) & 10 nJ/bit\(\cdot\)m\({}^{-2}\)) \\ \(\varepsilon_{mp}\) & 0.0013 nJ/bit\(\cdot\)m\({}^{-4}\)) \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental setting. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Scenario** & **Number of Nodes** & **Methods** & **FND** & **HND** & **LND** \\ \hline \multirow{4}{*}{1} & & & LEACH & 55 & 221 & 534 \\  & & K-LEACH & 43 & 365 & 680 \\  & & IEECHS-WSN & 62 & 320 & 766 \\  & & RCH-LEACH & 57 & 225 & 544 \\  & & DCK-LEACH & 254 & 485 & 904 \\ \hline \multirow{4}{*}{2} & & & LEACH & 51 & 212 & 524 \\  & & K-LEACH & 33 & 398 & 581 \\  & & IEECHS-WSN & 61 & 340 & 810 \\  & & RCH-LEACH & 58 & 227 & 534 \\  & & DCK-LEACH & 248 & 654 & 1041 \\ \hline \multirow{4}{*}{3} & & & LEACH & 56 & 221 & 536 \\  & & K-LEACH & 36 & 396 & 623 \\ \cline{1-1}  & & IEECHS-WSN & 60 & 322 & 799 \\ \cline{1-1}  & & RCH-LEACH & 61 & 227 & 538 \\ \cline{1-1}  & & DCK-LEACH & 238 & 667 & 1058 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison FND, HND, LND of LEACH, K-LEACH, IEECHS-WSN, RCH-LEACH, and DCK-LEACH. In scenario 1 of Figure 3, the LEACH algorithm has the minimal cluster (only 2 nodes) after the first round of clustering, which may lead to uneven energy consumption between clusters. In K-LEACH, the numbers of member nodes in clusters range from 5 to 18, which varies greatly. In DCK-LEACH, the numbers of member nodes in clusters range from 7 to 12, and the maximum number of clusters (12 nodes) is reduced by six compared with that of the K-LEACH algorithm (18 nodes). It shows that the numbers of member nodes in clusters fluctuate little, which means more balance in terms of energy consumption of cluster-heads within clusters. In K-LEACH of scenario 2, it shows that nodes which are very close to each other (see the nodes within red circles), are not grouped in the same cluster, but join in four rather distant clusters in Figure 3. In DCK-LEACH, the algorithm exactly groups these nodes in the same cluster. This will greatly save energy consumption in data transmission and thus extend the network lifetime. Scenario 3 of Figure 3 shows that as the number of nodes in the network increases, the LEACH algorithm generated the maximum clusters (49 nodes) and the minimum clusters (7 nodes). Due to the random selection of cluster-heads in LEACH, it is more prone to generating super-scale clusters that significantly shorten the network lifetime. K-LEACH generates the maximum cluster (40 nodes), while the DCK-LEACH algorithm divides these 40 nodes into two clusters, which makes the sizes of clusters more uniform and reduces the energy consumption. For the results of the LEACH algorithm in all scenarios, since LEACH selects cluster-heads randomly, once the selected cluster-heads are too close to each other, the maximum or the minimum clusters will be generated, which results in the uneven distribution of energy consumption within the clusters. Cluster-heads with a large number of member nodes would be overburdened which leads to premature death.