Provided are a computer program product, system, and method to determine whether to perform entity resolution on vertices in an entity graph. A determination is made of pairs of records in a database having a relationship value satisfying a threshold. An entity relationship graph has a vertex for each of the records of the pairs and an edge between two vertices. Each vertex has a self-information score based on content in the record, an initial unique entity identifier, and an entity information score. For each subject vertex of the vertices, a determination is made of a target vertex directly connected to the subject vertex that has a highest entity information score and whether to set the subject vertex entity identifier and entity information score to the entity identifier and entity information score of the target vertex based on the target vertex self-information score.