Adhesive interactions between nanofibers strongly influence the mechanical behavior of soft materials composed of fibrous networks. We use atomic force microscopy in lateral force mode to drag a cantilever tip through fibrous networks, and use the measured lateral force response to determine the adhesive forces between fibers of the order of 100 nm diameter. The peaks in lateral force curves are directly related to the detachment energy between two fibers; the data is analyzed using the Jarzynski equality to yield the average adhesion energy of the weakest links. The method is successfully used to measure adhesion forces arising from van der Waals interactions between electrospun polymer fibers in networks of varying density. This approach overcomes the need to isolate and handle individual fibers, and can be readily employed in the design and evaluation of advanced materials and biomaterials which, through inspiration from nature, are increasingly incorporating nanofibers. The data obtained with this technique may also be of critical importance in the development of network models capable of predicting the mechanics of fibrous materials.