Connectivity Assessment of Random Directed Graphs with Application to Underwater Sensor Networks

In this brief, the problem of connectivity assessment for a random network is investigated. The weighted vertex connectivity (WVC) is introduced as a metric to evaluate the connectivity of the weighted expected graph of a random sensor network, where the elements of the weight matrix characterize the operational probability of their corresponding communication links. The WVC measure extends the notion of vertex connectivity (VC) for random graphs by taking into account the joint effects of path reliability and network robustness to node failure. The problem of computing the WVC measure is transformed into a sequence of iterative deepening depth-first search and maximum weight clique problems. An algorithm is developed accordingly to find the proposed connectivity metric. The approximate WVC measure is defined subsequently as a lower bound on the introduced connectivity metric which can be found by applying a polynomial-time shortest path algorithm in a sequential manner. The performance of the proposed algorithms is validated using an experimental underwater acoustic sensor network.