Node similarity is fundamental in graph analytics. However, node similarity between nodes in different graphs (inter-graph nodes) has not received enough attention yet. The inter-graph node similarity is important in learning a new graph based on the knowledge extracted from an existing graph (transfer learning on graphs) and has applications in biological, communication, and social networks. In this paper, we propose a novel distance function for measuring inter-graph <u>n</u>ode similarity with <u>e</u>dit <u>d</u>istance, called NED . In NED, two nodes are compared according to their local neighborhood topologies which are represented as unordered k -adjacent trees, without relying on any extra information. Due to the hardness of computing tree edit distance on unordered trees which is NP-Complete, we propose a modified tree edit distance, called TED* , for comparing unordered and unlabeled k -adjacent trees. TED* is a metric distance, as the original tree edit distance, but more importantly, TED* is polynomially computable. As a metric distance, NED admits efficient indexing, provides interpretable results, and shows to perform better than existing approaches on a number of data analysis tasks, including graph deanonymization. Finally, the efficiency and effectiveness of NED are empirically demonstrated using real-world graphs.