This paper develops a novel object based graph model for semantic video comparison. The model describes a video with detected objects as nodes, and relationship between the objects as edges in a graph. We investigated several spatial and temporal features as the graph node attributes, and different ways to describe the spatial-temporal relationship between objects as the edge attributes. To tackle the problem of erratic camera motion on the detected object, a global motion estimation and correction approach is proposed to reveal the true object trajectory. We further propose to evaluate the similarity between two videos by establishing the object correspondence between two object graphs through graph matching. The model is verified on a challenging user generated video dataset. Experiments show that our method outperforms other video representation frameworks in matching videos with the same semantic content. The proposed object graph provides a compact and robust semantic descriptor for a video, which can be used for applications such as video retrieval, clustering and summarization. The graph representation is also flexible to incorporate other features as node and edge attributes.