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Transformers have become widely used in modern models for various tasks such as natural language processing and machine vision. This paper, proposes Gransformer, an algorithm for generating graphs that takes advantage of the transformer. We extend a simple autoregressive transformer encoder to exploit the structural information of the graph through efficient modifications. The attention mechanism is modified to consider the presence or absence of edges between each pair of nodes. We also introduce a graph-based familiarity measure that applies to both the attention and the positional coding. This autoregressive criterion, inspired by message passing algorithms, contains structural information about the graph. In the output layer, we also use a masked autoencoder for density estimation to efficiently model the generation of dependent edges. We also propose a technique to prevent the model from generating isolated nodes. We evaluate this method on two real-world datasets and compare it with some state-of-the-art autoregressive graph generation methods. Experimental results have shown that the proposed method performs comparative to these methods, including recurrent models and graph convolutional networks.