## 6 Simulations and Discussion
### The Effect of Merging/Splitting Clusters  
Given the network density, the node mobility, and the cluster formation parameters, Figure 13 (left) depicts the comparison of the initial cluster formation and the stable one for different settings of cluster parameters and Figure 13 (right) describes the frequency of cluster merging and splitting in a network over a time period of 200 seconds. As shown in Figure 13, the number of cluster reformation operation naturally decreases and the network topology towards to be stable as time proceeds.  
Figure 14 (left) depicts the number of clusters when merging and splitting are employed for different transmission ranges. Compared with the cluster formation using a large transmission range, a short transmission range results in a larger number of clusters since the sensors may be isolated or form clusters locally. Moreover, when the transmission range is large, the large cluster range may leads to unbalanced load among clusters. Therefore, in order to achieve load balancing in each cluster, the merge and split technique can be applied to reorganize the network. With merging and splitting, Figure 14 (right) illustrates that when compared to the network topology without cluster reformation, the topology with cluster reorganization has less clusters, which further stabilize the network operation with a small variation in the number of clusters.  
Figure 15 shows the comparison of a typical network topology applying the proposed scheme (left) and that using the MOBIC algorithm (right). As mentioned in Section 2., MOBIC presents an aggregate local mobility metric for the cluster formation process such that mobile sensors with low relative speed have the chance to become clusterheads. However, it may not work well in a dynamic environment due to the disregard of mobility manners in cluster maintenance. On the other hand, the proposed approach configures the network autonomously with cluster formation parameters and considers mobility manners in cluster reformation phase when facing the topology changes, which manages the topology effectively.  
Figure 12: Average number of clusterhead (left) and gateway (right) changes with varying the node mobility and the cluster constraint parameters; the number of sensors \(n=200\) and \(R_{\mathcal{M}}=10.5\).  
Figure 14: The frequency of cluster merging and splitting in a network given the network density \(n=200\) with varying the node mobility and the cluster formation parameters (left); the comparison of the network topology without cluster reformation and the network topology with cluster reformation given the network density \(n=200\), the transmission range \(R_{\mathcal{M}}\), the node mobility = 2 m/sec, and the cluster formation parameters (_LB_ = 4, \(z\) = 8, and _UB_ = 12) (right).  
Figure 13: The comparison of the initial cluster formation (filled symbol) and the stable one (hollow symbol) for different settings of cluster parameters (left); the number of cluster merging and splitting in a network given the network density \(n=200\), \(R_{\mathcal{M}}=10.5\), the mean node mobility = 2 m/sec, and the cluster formation parameters (_LB_ = 4, \(z\) = 8, and _UB_ = 12).