Whether y obtains under the counterfactual supposition that x is thought to depend on whether y obtains in the most similar world(s) in which x obtains. Graphical causal models have proved useful in developing a principled notion of similarity between worlds, but this notion is limited insofar as it does not apply to counterfactual suppositions about causal structure. Here, we explore the possibility of filling this lacuna by introducing a notion of similarity between causal graphs. Since there are multiple principled senses in which graphs can be similar, we introduce multiple similarity metrics and multiple ways to prioritize these metrics.