Using detailed administrative microdata for two countries, we build a modeling framework that yields new explanations for the origin of firm sizes, the firm contributions to unemployment, and the job-to-job mobility of workers between firms. Firms are organized as nodes in networks where connections represent low mobility barriers for workers. These labor flow networks are determined empirically, and serve as the substrate in which workers transition between jobs. We show that highly skewed firm size distributions are predicted from the connectivity of firms. Further, our model permits the reconceptualization of unemployment as a local network phenomenon related to both a notion of firm-specific unemployment and the network vicinity of each firm. We find that firm-specific unemployment has a highly skewed distribution. In coupling the study of job mobility and firm dynamics the model provides a new analytical tool for industrial organization and makes it possible to synthesize more targeted policies managing job mobility.