Abstract Several methods have been developed for inferring gene-gene interactions from expression data. To date, these methods mainly focused on intra-cellular interactions. The availability of high throughput spatial expression data opens the door to methods that can infer such interactions both within and between cells. However, the spatial data also raises several new challenges. These include issues related to the sparse, noisy expression vectors for each cell, the fact that several different cell types are often profiled, the definition of a neighborhood of cell and the relatively small number of extracellular interactions. To enable the identification of gene interactions between cells we extended a Graph Convolutional Neural network approach for Genes (GCNG). We encode the spatial information as a graph and use the network to combine it with the expression data using supervised training. Testing GCNG on spatial transcriptomics data we show that it improves upon prior methods suggested for this task and can propose novel pairs of extracellular interacting genes. Finally, we show that the output of GCNG can also be used for down-stream analysis including functional assignment. Supporting website with software and data: https://github.com/xiaoyeye/GCNG .