Previous works mainly focused on estimating direct relationship strength in social networks. If two users are not directly connected in a social network, there is no direct relationship. In order to estimate the relationship strength between two indirectly connected users as well as directly connected users, this paper proposes an estimation method for relationship strength in weighted social network graphs, which is based on the trust propagation strategy and the estimation of direct relationship strength. Our method considers the length of a relationship path, the number of relationship paths and the edge weights (direct relationship strength) along with a relationship path to estimate the strength of indirect relationship. Then it synthesizes the direct and indirect relationship strength to represent the strength of relationship between two users in social net- works. Thus our method can fully estimate the relationship strength between any two users in a social network no matter whether they are directly connected or not.