Congestion in wireless ad-hoc and sensor networks not only causes packet loss, and increases queueing delay, but also leads to unnecessary energy consumption. In a wireless ad-hoc and sensor network, two types of congestion can occur: node-level congestion, which is caused by buffer overflow in the node, or link-level congestion, when wireless channels are shared by several nodes and collisions occur when multiple active nodes try to seize the channel at the same time.
We study a measure of link-level congestion in a static wireless ad-hoc and sensor network randomly deployed over an area. The measure considered on this paper is the inverse of the greatest eigenvalue of the adjacency matrix of the random graph. This measure of congestion gives an approximation of the average quantity of wireless links of a certain length that a node have on the wireless ad-hoc and sensor network. We review the results to find this measure of congestion in a Bernoulli random graph and we use tools from random graph theory and random matrix theory to extend this measure of congestion on a Geometric random graph.