A graph neighborhood consists of a set of nodes that are nearby or otherwise related to each other. While existing definitions consider the structure (or topology) of the graph, we note that they fail to take into account the information propagation and diffusion characteristics, such as decay and reinforcement, common in many networks. In this paper, we first define the propagation efficiency of nodes and edges. We use this to introduce the novel concept of zero-erasure (or impact) neighborhood (ZEN) of a given node, n, consisting of the set of nodes that receive information from (or are impacted by) n without any decay. Based on this, we present an impact neighborhood indexing (INI) algorithm that creates data structures to help quickly identify impact neighborhood of any given node. Experiment results confirm the efficiency and effectiveness of the proposed INI algorithms.