Title: Ego-CNN: An Ego Network-based Representation of Graphs Detecting Critical Structures. Abstract: While existing graph embedding models can generate useful embedding vectors that perform well on graph-related tasks, what valuable information can be jointly learned by a graph embedding model is less discussed. In this paper, we consider the possibility of detecting critical structures by a graph embedding model. We propose Ego-CNN to embed graph, which works in a local-to-global manner to take advantages of CNNs that gradually expanding the detectable local regions on the graph as the network depth increases. Critical structures can be detected if Ego-CNN is combined with a supervised task model. We show that Ego-CNN is (1) competitive to state-of-the-art graph embeddings models, (2) can nicely work with CNNs visualization techniques to show the detected structures, and (3) is efficient and can incorporate with scale-free priors, which commonly occurs in social network datasets, to further improve the training efficiency.