Reliability of network connectivity

One major benchmark of the network is to check its reliability. This can be completed by checking the graphs when the network is fully functioning but subject to failure. There is no known algorithm that can measure the reliability in a polynomial time, and hence measuring the reliability by means of simulation is a preferable choice. The goal of this paper is to check the network reliability, by means of simulation using different methods, first generating a network using the random graphs, and second generating a network using regular graphs. Within this paper, I will focus on the all-terminal problem in which a path between every pair of nodes is checked using the Union and Find method.