Recent advances of incorporating layout information, typically bounding box coordinates, into pre-trained language models have achieved significant performance in entity recognition from document images. Using coordinates can easily model the position of each token, but they are sensitive to manipulations in document images (e.g., shifting, rotation or scaling) which are common in real scenarios. Such limitation becomes even worse when the training data is limited in few-shot settings. In this paper, we propose a novel framework, LAGER, which leverages the topological adjacency relationship among the tokens through learning their relative layout information with graph neural networks. Specifically, we consider the tokens in the documents as nodes and formulate the edges based on the topological heuristics. Such adjacency graphs are invariant to affine transformations, making it robust to the common image manipulations. We incorporate these graphs into the pre-trained language model by adding graph neural network layers on top of the language model embeddings. Extensive experiments on two benchmark datasets show that LAGER significantly outperforms strong baselines under different few-shot settings and also demonstrate better robustness to manipulations.