Abstract—Wireless Sensor Networks (WSNs) are increasingly used in many applications. However, issues like topology, routing, energy, nodes distribution and density, and connection reliability are affecting their deployment. In this work, investigation into such parameters using shortest path first routing technique is carried out using MATLAB simulation in free space with ransom uniform nodes distribution. The principle of simulation is to select the best route based on node’s location and available energy to carry out data transmission. The investigation proved that as the number of WSN nodes grows, the number of discovered routes grows in a power relationship with the overall time of route discovery, which is accompanied by a decrease in the number of hops per route. The research also showed that as the distance between the source and destination nodes increases, the number of routes identified increases in an exponential relationship, as does the overall route discovery time and the number of hops per route. Also, the simulation results shows that there is a relationship between path loss and both distance, and number of WSN nodes, with exponential relationship between path loss and distance and power relationship between path loss and number of nodes. The work also established a logarithmic relationship between distance and number of WSN nodes. By relating path loss to both distance and nodes, energy consideration is being covered in this work as an indirect parameter that is affected by routes, distance, communication medium and number of nodes. The mathematical modeling indicates that there is a need to dynamically correlate distance between nodes, communication medium, node’s energy, and topology to enhance routing of exchanged messages and to enable lower energy consumption.