The connectivity between different agents is a basic requirement in the control problem of multi-agent systems. For a connected graph, the connectivity corresponding to a 2-hop neighbor graph remains uncertain. In this paper, we consider the problem of verifying the connectivity of 2-hop neighbor graph of a connected graph. The properties of 2-hop neighbor graph from certain basic graphs, such as tree and circle graphs are studied firstly, then arbitrary connected graphs are discussed to investigate the connectivity of the underlying 2-hop neighbor graphs. The necessary and sufficient condition for verifying the connectivity of 2-hop neighbor graphs is proposed. Also a systematic verification strategy is developed, which is able to verify the connectivity of the underlying 2-hop neighbor graph of an arbitrary graph with the computation complexity of O(|V|+|E|), comparing with algebraic solutions.