An Experimental Analysis of Minimum Cut Size in Wireless Sensor Networks

Wireless sensor networks (WSN) and their applications become more and more common as the technology advances. The emerging concepts of Internet of Things and the Industry 4.0 boost their popularity, too. But there are still dominant bottlenecks including battery lifetime, transmission range, routing issues and others. These limitations may cause permanent faults on nodes, and thus, cause exclusion of the nodes from the network, which eventually may disconnect the network. Minimum cut size, a metric regarding the edge-connectivity of a graph, can be used to measure the reliability of a WSN. This work discusses that role of the minimum cut size; and more importantly, presents the results of a fundamental simulation showing the correlations between the total node count, the transmission range, and the achieved minimum cut size as an indicator of the maximum flow, in a randomly generated WSN topology. Our simulation results showed that at least 100 nodes with a transmission range of 140 m are required to create a random connected network on a field of $1000\times 1000\ \mathbf{m}$ area. If the ranges of the nodes be 80 m, then at least 200 nodes should be distributed on the field to expect a reliable connected network.