To effectively measure the strength of the directed relationship among the users in social network, based on the directed interaction frequency, a smooth model for computing the interaction strength of the user was proposed. Furthermore, user interaction strength was taken as dependent variable and user relationship strength was taken as latent variable, a latent regression model was constructed, and an Expectation-Maximization (EM) algorithm for parameter estimation of the latent regression model was given. Comprehensive experiments were conducted on two datasets extracted from Renren and Sina Weibo in the aspects of the best friends and the intensity ranking. On Renren dataset, the result of TOP-10 best friends chosen by the proposed model was compared with that of manual annotation, the mean of Normalized Discounted Cumulative Gain (NDCG) of the model was 69.48%, the average of Mean Average Precision (MAP) of the model was 66.3%, both of the parameters were significantly improved; on Sina Weibo dataset, the range of infection spread by nodes with higher relationship strength increased by 80% compared to the other nodes. The experimental results show that the proposed model can effectively measure user relationship strength.