## 3 The Measurement Tools of Network Topology  
The clustering techniques manage the large size of the network effect and control traffic and improve the energy level of each node. Faulty nodes can be easily identified in a cluster and automatically replaced by a suitable algorithm. In the cluster network, [PERSON] et al. [28], the graphical method G (N, E) is represented. Here, N is the number of nodes in the cluster, and E is the total energy utilized to transmit the packet from node i to j and i,j \(\in\) N. CH energy is evaluated by the residual energy of the node E\({}_{\text{RI}}\). The residual energy E\({}_{\text{RI}}\) is calculated from the total energy of the node to the utilized energy of the node and distance d\({}_{\text{ij}}\) is equal to the velocity of sending the packet to the time required to send all the packets from i to j. The Energy required to transmit one packet E\({}_{\text{P}}\) and a Total number of packets P\({}_{\text{n}}\). \[\text{E}_{\text{CH}}=\frac{\text{E}_{\text{RI}}}{\sum_{\text{j}=1}^{n}((\text{ d}_{\text{ij}}+(\text{E}_{\text{P}}\times\text{P}_{\text{n}}))} \tag{1}\]  
The data packet travels from one sensor node to another sensor node and is significantly observed in the network. Particularly, the data throughput of the network is evaluated from the amount of data transferred between the source and destination within a second. The time, [PERSON] et al. [29] is considered depending on the state of the node. At some point, the node acts as inactive, sleeping and idle. The total time is regarded as,  
\[\text{T}_{\text{Total}}=\text{T}_{\text{Active}}+\text{T}_{\text{Sleep}}+\text {T}_{\text{idle}} \tag{2}\]  
In active mode, nodes start to transfer and receive the packet with less delay. But few nodes enter sleep mode because of a less level of energy and other nodes act in idle mode. It takes a bit more time to complete the packet transmission and receive, [PERSON] et al. [29]. The active time is evaluated by the total bandwidth of the sender-to-receiver channel and the total number of nodes within a network  
\[\text{T}_{\text{Active}}=\frac{\sum_{\text{i}}^{\text{n}}\text{BW}_{\text{ij} }}{\text{N}_{\text{ij}}} \tag{3}\]Distance is very important in the routing algorithm; the shorter distance brings the data to the destination in less time. In this work, the distance is calculated as the sum of the distance between the adjacent node from i to j, and the total transfer and receive time of the packet. The bandwidth, S M, B et al. [30] is the capability of the route to take the data  
\[\mathrm{D_{\bar{\mathrm{\mathrm{\eta}}}}}=\sum_{\mathrm{a=1}}^{\mathrm{j}} \mathrm{d_{\bar{\mathrm{\mathrm{\eta}}}}}\mathrm{per\;Seconds}\bigg{(}\mathrm{ T_{Total}\;(Sec)\times\frac{1\;min}{60\;Seconds}}\bigg{)} \tag{4}\]  
The total residual energy, S M, B et al. [30] of the network is taken into account by the energy of the cluster network and the remaining energy of the MANET route. \[\mathrm{E_{T=\sum_{\mathrm{r=1}^{n}\;(E_{CH}+E_{MANET})}}} \tag{5}\]  
where r is the route between the sender and destination, and \(E_{CH}\) is CH residual energy. The MANET discovered the route's residual energy determined by the sum of the energy level between the adjacent links. The energy level of each link is calculated from the residual energy of the packet sent and received. The hop count of the source sensor node to the destination node is evaluated on all the discovered routes in MANET. The hop count is evaluated between the adjacent sequential nodes from the sensor to the destination. Sequential count details are collected from the route discovery process. Different types of routing algorithms provide more than one number of routes to reach the gateway node discovered by any one of the routing algorithms. However, the trusted route (R\({}_{t}\)) offers long life, less time delay, reduced packet loss and improved performance of the system, [PERSON] et al. [31].