Graphs are an intuitive and natural way of representing handwriting. Due to their high representational power, they have shown high performances in different learning-free document analysis tasks. While machine learning is rather unexplored for graph representations, geometric deep learning offers a novel framework that allows for convolutional neural networks similar to the image domain. In this work, we show that the concept of attribute prediction can be adapted to the graph domain. We propose a graph neural network to map handwritten word graphs to a symbolic attribute space. This mapping allows to perform query-by-example word spotting as it was also tackled by other learning-free approaches in the graph domain. Furthermore, our model is capable of query-by-string, which is out of scope for other graph-based methods in the literature. We investigate two variants of graph convolutional layers and show that learning improves performances considerably on two popular graph-based word spotting benchmarks.