Abstract: We introduce an analytical model for Erdős–Rényi graphs called GRE and derive expressions approximating its adjacency matrix. We then find expressions approximating its l-path matrix. After formulating key graph measures such as the clustering coefficient, the distance matrix, and the average shortest distance in terms of the l-path matrix, we deduce analytical expressions approximating them. Our expressions do not contain any free parameters and show fast convergence valid non-asymptomatically over the entire probability space. The proposed approach is generalizable to other random graphs and can be used to approximate algebraically well-defined graph measures to investigate finite-sized real-world networks.