Molecular dynamics simulations in conjunction with a number of network analysis techniques have been carried out to explore the structure of the hydrogen-bond (H-bond) network in mixtures of formamide (FA) and methanol (MeOH) across the entire composition range. Radial distribution functions and pair energy distributions have been utilized for a general insight into the localized interactions. A comprehensive understanding of the structural properties of the H-bond networks including FA…FA, MeOH…MeOH, and FA…MeOH H-bonding interactions has been obtained collectively from the distribution of H-bonds, extended neighborhood analysis, and the geodesic distance distribution. These analyses indicate that formamide molecules prefer formamide molecules not only as immediate hydrogen-bonded neighbors but also as neighbors in their extended neighborhood that spans the neighbors of the immediate neighbors. Methanol molecules are found not to show a strong preference for either of the molecule types. The network analyses utilized in this study reveal that the population and the topological length of chain-like H-bond pathways formed by FA molecules increase with the addition of small amounts of methanol until the mole fractions of each species are equal.