Abstract Overlapping community detection has drawn much attention recently since it allows nodes in a network to have multiple community memberships. A standard framework to deal with overlapping community detection is Matrix Factorization (MF). Although all existing MF-based approaches use links as input to identify communities, the relationship between links and communities is still under-investigated. Most of the approaches only view links as consequences of communities (community-to-link) but fail to explore how nodes’ community memberships can be represented by their linked neighbors (link-to-community). In this paper, we propose a Homophily-based Nonnegative Matrix Factorization (HNMF) to model both-sided relationships between links and communities. From the community-to-link perspective, we apply a preference-based pairwise function by assuming that nodes with common communities have a higher probability to build links than those without common communities. From the link-to-community perspective, we propose a new community representation learning with network embedding by assuming that linked nodes have similar community representations. We conduct experiments on several real-world networks and the results show that our HNMF model is able to find communities with better quality compared with state-of-the-art baselines.