Vertex similarity measure is a useful tool to discover the hidden relationships of vertices in a complex network. We introduce relation strength similarity (RSS), a vertex similarity measure that could better capture potential relationships of real world network structure. RSS is unique in that is is an asymmetric measure which could be used for a more general purpose social network analysis; allows users to explicitly specify the relation strength between neighboring vertices for initialization; and offers a discovery range parameter could be adjusted by users for extended network degree search. To show the potential of vertex similarity measures and the superiority of RSS over other measures, we conduct experiments on two real networks, a biological network and a coauthorship network. Experimental results show that RSS is better in discovering the hidden relationships of the networks.