Along with generative AI, interest in scene graph generation (SGG), which comprehensively captures the relationships and interactions between objects in an image and creates a structured graph-based representation, has significantly increased in recent years. However, relying on object-centric and dichotomous relationships, existing SGG methods have a limited ability to accurately predict detailed relationships. To solve these problems, a new approach to the modeling multiobject relationships, called edge dual scene graph generation (EdgeSGG), is proposed herein. EdgeSGG is based on a edge dual scene graph and Dual Message Passing Neural Network (DualMPNN), which can capture rich contextual interactions between unconstrained objects. To facilitate the learning of edge dual scene graphs with a symmetric graph structure, the proposed DualMPNN learns both object- and relation-centric features for more accurately predicting relation-aware contexts and allows fine-grained relational updates between objects. A comparative experiment with state-of-the-art (SoTA) methods was conducted using two public datasets for SGG operations and six metrics for three subtasks. Compared with SoTA approaches, the proposed model exhibited substantial performance improvements across all SGG subtasks. Furthermore, experiment on long-tail distributions revealed that incorporating the relationships between objects effectively mitigates existing long-tail problems.