The purpose of graph embedding is to learn a lower-dimensional embedding function for graph data. Existing methods usually rely on maximum likelihood estimation (MLE), and often learn an embedding function through conditional mean estimation (CME). However, MLE is well-known to be vulnerable to the contamination of outliers. Furthermore, CME might restrict the applicability of the graph embedding methods to a limited range of graph data. To cope with these problems, this paper proposes a novel method for graph embedding called the robust ratio graph embedding (RRGE). RRGE is based on the ratio estimation between the conditional and marginal probability distributions of link weights given data vectors, and would be applicable to a wider-range of graph data than CME-based methods. Moreover, to achieve outlier-robust estimation, the ratio is estimated with the γ-cross entropy, which is a robust alternative to the standard cross entropy. Numerical experiments on artificial data show that RRGE is robust against outliers and performs well even when CME-based methods do not work at all. Finally, the performance of the proposed method is demonstrated on realworld datasets using neural networks.