Group fairness is a popular approach to prevent unfavorable treatment of individuals based on sensitive attributes such as race, gender, and disability. However, the reliance of group fairness on access to discrete group information raises several limitations and concerns, especially with regard to privacy, intersectionality, and unforeseen biases. In this work, we propose a "group-free" measure of fairness that does not rely on sensitive attributes and, instead, is based on homophily in social networks, i.e., the common property that individuals sharing similar attributes are more likely to be connected. Our measure is group-free as it avoids recovering any form of group memberships and uses only pairwise similarities between individuals to define inequality in outcomes relative to the homophily structure in the network. We theoretically justify our measure by showing it is commensurate with the notion of additive decomposability in the economic inequality literature and also bound the impact of non-sensitive confounding attributes. Furthermore, we apply our measure to develop fair algorithms for classification, maximizing information access, and recommender systems. Our experimental results show that the proposed approach can reduce inequality among protected classes without knowledge of sensitive attribute labels. We conclude with a discussion of the limitations of our approach when applied in real-world settings.