The Shane-Wirtanen galaxy count catalog gives the strong visual impression of large-scale linear or filamentary features in the galaxy distribution. Computer simulations of hierarchical galaxy clustering constructed to have two-, three-, and four-point autocorrelation functions like those observed do not have such an appearance. A simple and well-defined algorithm which maps and quantifies filamentary structure is developed. It appears to be successful in identifying those filaments which the eye picks out in the Shane-Wirtanen catalog and thus provides an objective tool for studying these structures. A catalog and map of the most prominent Shane-Wirtanen filaments is given. The application of the algorithm to a computer simulation of hierarchical galaxy clustering is described.