Agents interactions in a social network are dynamic and stochastic. We model the dynamic interactions using the hidden Markov model, a probability model which has a wide array of applications. The transition matrix with three states, forgetting, reinforcement and exploration is estimated using simulation. Singular value decomposition estimates the observation matrix for emission of low, medium and high interaction rates. This is achieved when the rank approximation is applied to the transition matrix. The initial state probabilities are then estimated with rank approximation of the observation matrix. The transition and the observation matrices estimate the state and observed symbols in the model. Agents interactions in a social network account for between 20% and 50% of all the activities in the network. Noise contributes to the other portion due to interaction dynamics and rapid changes observable from the agents transitions in the network. In the model, the interaction proportions are low with 11%, medium with 56% and high with 33%. Hidden Markov model has a strong statistical and mathematical structure to model interactions in a social network.