The core of recommendation models is estimating the probability that a user will like an item based on historical interactions.Existing collaborative filtering (CF) algorithms compute the likelihood by utilizing simple relationships between objects,e.g.,user-item,item-item,or user-user.They always rely on a single type of object-object relationship,ignoring other useful relationship information in data.In this paper,we model an interaction between user and item as an edge and propose a novel CF framework,called learnable edge collaborative filtering (LECF).LECF predicts the existence probability of an edge based on the connections among edges and is able to capture the complex relationship in data.Specifically,we first adopt the concept of line graph where each node represents an interaction edge;then calculate a weighted sum of similarity between the query edge and the observed edges (i.e.,historical interactions) that are selected from the neighborhood of query edge in the line graph for a recommendation.In addition,we design an efficient propagation algorithm to speed up the training and inference of LECF.Extensive experiments on four public datasets demonstrate LECF can achieve better performance than the state-of-the-art methods.