A spatial graph is a specific type of graph with spatial attributes associated with the nodes and the edges. It is a smart modelling choice for capturing the skeleton of a shape, a blood vessel network, a porous tissue, and many other data objects with intrinsically complex geometry. In this talk, we describe how spatial graphs can be analysed using a specific metric (the Fused Gromov–Wasserstein metric). We extend a testing procedure between distributions of spatial graphs, a depth measure to describe the distribution of spatial graphs, and a dimensionality reduction procedure based on preserving key topological features. We present this variety of methods on a dataset of cardiac fibrosis tissue and on a dataset of fungus mycelium networks.