## 1 Introduction  
In many critical applications, tiny wireless objects, known as sensor nodes, have been exploited to improve the network coverage and communications [1; 2; 3; 4]. Sensor nodes are operated in dynamic, ad-hoc and self-configured mode to gather environmental data. Due to limited energy, transmission and memory constraints, the field of WSN is to make them different from traditional networks. Among all the constraints, the energy consumption gained much research interest in improving the performance of networks. Sensor nodes transmit their data towards the BS using an appropriate proxy node, also called a gateway or cluster head [5; 6; 7; 8]. Due to its extra burden, the cluster heads consume energy resources more rapidly than other nodes. Such a problem mostly creates a routing hole in the network regions and results in packet drop ratios with network latency. Normally, the data routing of static sensors in the comparison of mobile sensors is most suitable for the small-sized region due to predefined data forwarding paths. While in the scenario of a large region, mobile nodes are preferred due to their mobility, scalability and coverage characteristics [9; 10; 11; 12]. In recent years, the technology of machine learning improved the monitoring of targeting fields and learned the data routing due to their intelligent and lightweight processes. The area of machine learning makes the environment for low-powered sensor nodes more robust, cost-effective and energy-efficient. The hierarchical schemes divide similar nodes based on certain conditions into various clusters [13; 14; 15; 16]. A cluster is a particular region and nodes are bounded to communications with BS through cluster heads. The clusters can be achieved using either one of the two approaches, i.e., top-down and bottom-up. Within each cluster, one node is assigned a primary duty for data aggregation and forwarding, such node is called cluster head [17; 18]. However, the energy of cluster heads is consumed most swiftly due to their computational, processing and transmission powers in the data routing. Thus, clustering nodes and uniformly distribute the load among cluster heads are major research problems for network efficacy [19; 20]. Along with securing the sensors' data against attackers, the efficient generation and distribution of keys for transmission sessions are other important concerns [21; 22; 23; 24]. This paper presents an energy-aware graph clustering and intelligent routing protocol using a supervised system to address the restrictions of existing energy-efficient routing solutions. The EGCIR protocol exploits a centralized cluster formation with the selection of energy-efficient and robust cluster heads, which results in minor network overhead and communication cost. The EGCIR protocol makes use of a supervised machine learning algorithm to share the sensors into various clusters and make the network smarter. Furthermore, it avoids the consumption of additional energy of sensors due to forwarding of control and route request messages. Moreover, it introduces fault-tolerant routing paths between cluster heads using a graph-based technique and achieves an optimized network lifetime. In addition, it offers a secure mechanism to obtain trustworthiness and authentic communications between the intracluster and intercluster transmission. The encryption keys are generated and distributed in the hierarchy from the BS to cluster heads and from cluster heads to sensor nodes. The malicious entities are adversaries and they aim to prevent sensor nodes to attain network services reliably. The proposed solution also excludes such malicious nodes from the existing routes and makes the transmission links more intellectual using security methods. The simulation experiments demonstrate improved outcomes of the EGCIR protocol in the comparison of existing solutions.