In this paper, we use tools from network theory to trace the properties of the matching function to the structure of granular connections between applicants and vacancies. We unify seemingly disparate parts of the literature by recovering multiple functional forms as special cases including the CES. We derive a testable condition under which matching in any network from the broad class we analyze can be thought "as if" it comes from a CES matching function, up to a first-order approximation. We provide a theory of match efficacy in which inequality in search intensities is the key determinant of how well the matching process works. A robust finding of our analysis is that dispersion of search intensities on either side of the market is bad for the matching process. We also show that a rise in the market's mean search intensity can reduce match efficacy when it is associated with a higher Gini coefficient of search intensities.