Computing similarity of two graphs with partially overlapping sets of nodes


Consider two graphs $ G_1 = (E_1, V_1) $ and $ G_2 = (E_2, V_2)$ with their associated sets of edges $ E$ and nodes $ V$ . I’m familiar with concepts such as edit distance for computing the similarity/distance between these two graphs. I was wondering if there are any metrics for estimating similarity between graphs where they contain only partially overlapping sets of nodes, for example, if $ V_1 = (A, B, C) $ and $ V_2 = (B, C, D)$ .