## 3 Methodology
### Number of Alive Nodes  
Figure 9a displays the number of alive nodes in the proposed NBEER protocol, while Figure 9b and Table 10 compare the number of alive nodes between NBEER, Co-UWSN, and CEER. NBEER demonstrates a higher number of alive nodes, indicating its effectiveness in maintaining network connectivity.  
In NBEER, the higher number of alive nodes can be attributed to the minimal energy consumption and efficient cooperation between nodes, enabling easy data transfer to the sink node. Conversely, in CEER and Co-UWSN, clustering with cooperation leads to increased energy consumption. This is primarily because these techniques involve a multi-step process where clusters are first formed, cluster heads are then selected based on maximum energy, and subsequent cooperation among cluster heads takes place. Such lengthy procedures result in higher energy consumption and depletion of node energy.  
In our proposed technique, we address these issues by introducing a more streamlined approach. Instead of forming clusters and selecting cluster heads, nodes directly choose neighboring nodes as head nodes. Data are then transferred from the nodes to the selected head nodes, and the head nodes transmit the data directly to the sink node. This approach significantly reduces energy consumption as only a single node, the NHN (neighboring head node), is responsible for transmitting data. As a result, the remaining nodes conserve their energy and remain unaffected. Figure 10 presents a comparison of the average values, highlighting NBEER's superiority in terms of the number of alive nodes. This underscores the efficacy of neighbor node cooperation and NHN selection in NBEER, contributing to enhanced network longevity and connectivity. In summary, NBEER's neighbor node cooperation and NHN selection led to a higher number of alive nodes, optimizing energy utilization and bolstering network vitality. The comparison in Figure 10 reinforces NBEER's advantage in sustaining a robust underwater wireless sensor network infrastructure.  
**Protocol** & & **After** & **After** & **After** & **After** & **After** & **After** & **After** & **After** & **After** & **After** & \\  & & **1000 s** & **2000 s** & **3000 s** & **4000 s** & **5000 s** & **6000 s** & **7000 s** & **8000 s** & **9000 s** & **10,000 s** & \\
**Co-** & **551** & **225** & **217** & **207** & **191** & **170** & **168** & **160** & **150** & **139** & **135** & **176.2** \\
**UWSN** & **529** & **215** & **209** & **204** & **198** & **182** & **180** & **178** & **172** & **168** & **167** & **187.3** \\
**NBEER** & **633** & **220** & **218** & **212** & **203** & **198** & **195** & **192** & **184** & **181** & **180** & **198.3** \\ \hline \hline \end{tabular}
\end{table}
Table 10: The number of alive nodes and average alive nodes after 10,000 s.  
Figure 9: (a) Alive nodes analysis of NBEER (b) Alive Node of all protocols versus network lifetime (s).  
* Iterations of neighboring and Dispersion of Neighbor Head Nodes  
The algorithmic overhead is influenced by the number of iterations involved in the compilation process. By reducing the iterations per round, the build time and the number of transmitted packets can be minimized. The relationship between the initial value 0 and the neighboring node (NN) numbers, denoted as \"n\", becomes apparent when considering two different values, denoted as \"w\" and \"y\". When both \"w\" and \"y\" are set to 0, the minimum number of NNs required to increase the CR (communication reliability) is achieved. As the NN count increases, the minimization of \"w\" and \"y\" values in CR becomes crucial. In our proposed method, the values of \"w\" and \"y\" are both set to 1, and a CR value of 60 is assigned. The battery life of the nodes within the network is dependent on the total number of nodes present.