We present an efficient matching method for generalized geometric graphs. Such graphs consist of vertices in space connected by curves and can represent many real world structures such as road networks in remote sensing, or vessel networks in medical imaging. Graph matching can be used for very fast and possibly multimodal registration of images of these structures. We formulate the matching problem as a single player game solved using Monte Carlo Tree Search, which automatically balances exploring new possible matches and extending existing matches. Our method can handle partial matches, topological differences, geometrical distortion, does not use appearance information and does not require an initial alignment. Moreover, our method is very efficient-it can match graphs with thousands of nodes, which is an order of magnitude better than the best competing method, and the matching only takes a few seconds.