## 8 Simulation  
### Experimental Settings  
The performances of the proposed approach are analyzed and compared using a simulator implemented in java using Java Universal Network/Graph (JUNG) [57] a Java based library that allows the modeling, analysis, and visualization of a wireless network as a graph. The network topology is composed of a variable number of nodes (\(\delta\in[40,1300]\)) distributed across a square area of size \(\Delta^{2}\) = 1000 \(\times\) 1000 m\({}^{2}\). A random distribution is assumed to generate a random network topology, which is typically used in clustering approaches in the literature to approximate a real deployment scenario. Conventional sensor network usually uses wireless communication standard with low power consumption [58], such as IEEE 802.15.4 Zigbee (with a maximum transmitting distance of 100 m) or the 802.11n [28] (with a transmitting distance of 70 m). Therefore, based on the wireless communication standards used by regular wireless networks, in this experiment, we assume that network nodes have a transmission range of \(Tr=70\) m. We use the classic UnitDisk Graph (UDG) connectivity model [59] where communication links are symmetric, i.e., a wireless communication link exists between two nodes \(i\) and \(j\) if they are within each other's transmission range (\(Dist(i,j)\leq Tr_{j}\wedge Dist(j,i)\leq Tr_{i}\)). The energy model used is described in Section 5, node has 1 joule of initial energy and the size of a data packet is \(l=100\) bytes. The k-hop clustering decreases the number of reconfiguration events that may occur inside the cluster [20]. Therefore, instead of using a periodic CH rotation for load balancing. In this study, the CH rotation occurs when the weight of the current CH is exceeded by one of its k-hop neighbors, which means that the current cluster has undergone a considerable topology changes. This mechanism avoids the quick alternation of CHs and further reduces the number of clustering messages generated. The experiment parameters are listed in Table 4. Increasing the number of communication hops inside each cluster generates long routing paths which may extensively increase the data transmission delay. Thereby, the performance of our clustering algorithm is analyzed by considering \(k\in\{1,2,3\}\). The k-hop constraint ought to be specified depending on the application requirements to improve the network performance. The proposed scheme is experimented with varying maximum hop values and different nodes density to analyze the network performance under different scenarios.  
In the following section, the performance of our approach DC2 HC is compared with two ubiquitous and recent protocols that belong to the same family of multi-hop clustering. MH-LEACH [46] and Mezghani protocol [34] are both used for the k-hop intra-clustering and their primary objective is to reduce the waste of energy and the number of generated clusters. Owing to these characteristics, these protocols are selected for the performance comparison to our proposed protocol.  
Five parameters are used for the performance analysis of the simulated protocols, namely, the cluster heads cardinality, the energy consumption, number of exchanged messages, the average network lifetime and the number of dead nodes. The same parameters are used to compare the three protocols. Each simulation result is the average of 10 measurements for each used metric with varying density and node distributions.