Technological advances for low-cost Wi-Fi applications such as ‘the wireless sensor network (WSN) deployment’ are at an advanced stage of acceptance, especially in smart home environments. The application of this kind of network is referred to as a wireless sensor home network (WSHN). In literature, the evaluation of customers' home wireless network performance level is usually done via real-time experiment or by experience to test the network’s performance, leading to network vendors able to gain reference performance for: improvement of their network capacity and the adoption of the emerging requirement of Wi-Fi services. However, the usual practice of comparison of energy consumption in WSHN applications is by developing WSHN systems for information transmission and reception in the home network to measure delay, throughput and energy consumption performance metrics using heuristics and intuition approaches. This work shows that real-time-based performance measurements of WSHN systems should be first carried out using the formal analytical method; before simulation and real-time experiments. Use of analytical method in WSHN provides users with a more defined idea of the kind of results to expect from their network simulations. To this end, this work presents an analytical method based on energy consumption for WSHN grid-based and line-based topology for the same metrics, with a description of each of the networks, which is first of its kind in WSHN. The work is further strengthened through simulation results. The results of our mathematical analysis show a variation of network energy consumption for single-hop and multi-hop communication for reference purposes for future WSHNs. The mathematical analysis results are futher validated by the simulation results of WSNs comprising of nodes using ESP32 microcontrolers RF specifications; where it shows that in most cases, using single-hop communication might cause excessive energy consumption in the network. This being more pronounced when the distance apart of the smart devices is above 50feet or the network nodes is above 20; more also, when the packet size is above 50 bits. In this case, multi-hop communication it is seen to be of preferable communication at a higher number of nodes, larger packet size and longer distance between devices. However, if the network size is small, there is little difference in the energy consumption between the two methods and it is in such networks where single-hop is preferred due to the reduced complexity of the network structure and small delay time of which promotes responsiveness of the network.