We assess the presumption that social networks reinforce inequality by providing high -wage workers' with preferential access to high-wage establishments. Our results based on very detailed Swedish register data contradict this view. We do show that high -wage job seekers tend to be connected to high-wage workers employed in high-wage establishments. Furthermore, social connections appear to directly cause the allocation of workers to jobs. But the sorting resulting from hires within social networks is less unequal than the sorting resulting from market hires, essentially because low-wage firms rely on social connections to hire high-wage workers.