Recent interests on XML, Semantic Web, and Web ontology, among other topics, have sparked a renewed interest on graph-structured databases. A fundamental query on graphs is the reachability test of nodes. Recently, 2-hop labeling has been proposed to index large collections of XML and/or graphs for efficient reachability tests. However, there has been few work on updates of 2-hop labeling. This is compounded by the fact that data may change over time. In response to these, this paper studies the incremental maintenance of 2-hop labeling. We identify the main reason for the inefficiency of updates of existing 2-hop labels. We propose three updatable 2-hop labelings, hybrids of 2-hop labeling, and their incremental maintenance algorithms. The proposed 2-hop labeling is derived from graph connectivity, as opposed to SET COVER which is used by all previous work. Our experimental evaluation illustrates the space efficiency and update performance of various kinds of 2-hop labeling. Our results show that the incremental maintenance algorithm can be two orders of magnitude faster than previous methods and the size of our 2-hop labeling can be comparable to the existing 2-hop labeling. We conclude that there is a natural way to spare some index size for update performance in 2-hop labeling.