Substructure similarity search is to retrieve graphs that approximately contain a given query graph. It has many applications, e.g., detecting similar functions among chemical compounds. The problem is challenging as even testing subgraph containment between two graphs is NP-complete. Hence, existing techniques adopt the filtering-and-verification framework with the focus on developing effective and efficient techniques to remove non-promising graphs. Nevertheless, existing filtering techniques may be still unable to effectively remove many “low” quality candidates. To resolve this, in this paper we propose a novel indexing technique, GrafD-Index, to index graphs according to their “distances” to features. We characterize a tight condition under which the distance-based triangular inequality holds. We then develop lower and upper bounding techniques that exploit the GrafD-Index to (1) prune non-promising graphs and (2) include graphs whose similarities are guaranteed to e...