Abstract: Given a query graph and a database of corpus graphs, a graph retrieval system aims to deliver the most relevant corpus graphs. Graph retrieval based on subgraph matching has a wide variety of applications, e.g., molecular fingerprint detection, circuit design, and question answering. In this setup, a corpus graph is relevant to a query graph, if this query graph is a subgraph of the corpus graph. Existing neural graph retrieval models compare the node or graph embeddings of the query-corpus pairs to compute the relevance scores between them. However, such models may not provide edge consistency between query corpus pairs. Moreover, they predominantly use symmetric relevance scores, which are not appropriate in the context of subgraph matching, since the underlying relevance score in subgraph search should be measured using the partial order induced by subgraph-supergraph relationship. Consequently, they show poor retrieval performance in the context of subgraph matching. In response, we propose ISONET, an interpretable neural edge alignment model, which is better able to learn the edge consistent mapping necessary for subgraph matching. Furthermore, we design a novel scoring mechanism which enforces an asymmetric relevance score specifically for subgraph matching. ISONET’s design enables it to identify the underlying subgraph in corpus graph, which is relevant to the given query graph. Our experiments on diverse datasets show that ISONET outperforms existing baseline models for graph retrieval. Additionally, ISONET can provide the interpretable alignments between query-corpus graph pairs during inference, despite being trained only using binary relevance labels during training, without any ground truth information about node or edge alignments.