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.

Key nodes discovery is very important for social network. Nowadays, most of methods of key nodes discovery do not take relationship strength of nodes into account. Social networks, in essence, are weighted networks because relationship strengths of nodes are different. In this paper, a new method to compute relationship strength of nodes based on node interactions was proposed, and the method combined local features with global features. A node activity degree using user behavior features was defined; as a result, social networks were represented as dual-weighted networks by taking relationship strength as edge weight and node activity as node weight. Based on PageRank algorithm, two improved algorithms were proposed. The node weights were used as damping coefficient, and the weight of the edges was used to compute importance of nodes during iterative process. Two datasets from different sources were selected and comprehensive experiments were conducted. The experimental results show that proposed algorithms can effectively discover key nodes in real social networks.