We develop a theory of unemployment in which workers search for jobs through a network of firms, the labor flow network (LFN). The lack of an edge between two companies indicates the impossibility of labor flows between them due to high frictions. In equilibrium, firms' hiring behavior correlates through the network, modulating labor flows and generating aggregate unemployment. This theory provides new micro-foundations for the aggregate matching function, the Beveridge curve, wage dispersion, and the employer-size premium. Using employer-employee matched records, we study the effect of the LFN topology through a new concept: `firm-specific unemployment'.