Inter-sentence relation extraction deals with a number of complex semantic relationships in documents, which require local, non-local, syntactic and semantic dependencies. Existing methods do not fully exploit such dependencies. We present a novel inter-sentence relation extraction model that builds a labelled edge graph convolutional neural network model on a document-level graph. The graph is constructed using various inter- and intra-sentence dependencies to capture local and non-local dependency information. In order to predict the relation of an entity pair, we utilise multi-instance learning with bi-affine pairwise scoring. Experimental results show that our model achieves comparable performance to the state-of-the-art neural models on two biochemistry datasets. Our analysis shows that all the types in the graph are effective for inter-sentence relation extraction.