## 2 Related Research Work
As the location of the neighboring nodes around the sink node are changed due to movement of the sink node, the probability of a hot-spot problem is reduced and network lifetime is improved due to a more even distribution of energy consumption in the surrounding nodes [37]. Keeping in view the node mobility, researchers have worked on the path formation for mobile sinks in [37; 38; 39] based on the predefined, controlled and random path selection procedures. In [40], [PERSON] et al. proposed a new routing aware algorithm to detect malicious nodes in a concealed data aggregation for WSNs to highlight the significance of data aggregation in WSNs by reducing communication overhead of sensor nodes. All these previous researches were formulated to equalize the energy consumption of nodes, but they are not able to prolong the network lifetime. Thus, an emerging concept \"utilization of working-sleeping cycle of nodes\" was introduced to improve the energy consumption of nodes and overall network lifetime [22]. The working-sleeping cycle can be segmented into two categories--synchronous and asynchronous working-sleeping cycles. Authors in [41; 42] revealed that synchronous working-sleeping cycle could help in achieving improvement in energy consumption. However, the synchronization problem needed significant contributions. Thus in [43], [PERSON] et al. proposed an energy efficient synchronization algorithm in which adaptive adjustment of the traffic and wakeup period could improve energy consumption through counter-based and exponential-smoothing algorithms. In addition to it, some researchers also explored asynchronous working-sleeping cycle in which all nodes have independent working-sleeping schedules depending on the network connectivity requirements in terms of traffic coverage area [16; 17]. [PERSON] et al. also proposed an asynchronous working-sleeping technique while focusing on network coverage by maintaining a minimum number of awake nodes [44]. As a result of working-sleeping cycle strategy, opportunistic node connections will be established between sensor nodes and the mobile sink which can further lead to link instability. Therefore, we need a random graph theory to model these kinds of opportunistic node connections in the WSN. [PERSON] et al. proposed reliable routing with distributed learning automaton (RRDLA) algorithm, which considers dynamics of links in finding a path from a source to a destination by considering Quality of Service (QoS) constraints such as end-to-end reliability and delay [45]. [PERSON] et al. in [46] presented a new opportunistic routing protocol called energy-efficient opportunistic routing protocol using a new forward list (EEOR-FL) aiming to balance energy consumption and maximize the network lifetime by calculating the list of candidates. [PERSON] et al. proposed a new collision-aware opportunistic routing protocol abbreviated as SCAOR for highways by utilizing cluster-based scheduling algorithms [47]. [PERSON] et al. in [48] indicated that WSN modeling in the case of working-sleeping cycle strategy and opportunistic node connections can be modeled using a random geometric graph in which a set of vertices represent sensor nodes and a set of edges represent links between those vertices or sensor nodes. In reference [49], [PERSON] et al. proposed a novel random graph modeling for heterogeneous sensor networks based on different transmission ranges and a new routing metric. Referring to [50], in which [PERSON] et al. focused on the challenges and weaknesses of using random graph theory for modeling WSN, they thus proposed a new weighted topology model for WSN based on the random geometric theory. In [51], [PERSON] et al. developed an optimal policy for connection between source and destination nodes in random WSN topology using random graph. For this policy to be implemented correctly, an energy efficient probe message forwarding mechanism was proposed.