Human relations are driven by social events-people interact, exchange information, share knowledge and emotions, and gather news from mass media. These events leave traces in human memory, the strength of which depends on cognitive factors such as emotions or attention span. Each trace continuously weakens over time unless another related event activity strengthens it. Here, we introduce a novel cognition-driven social network (CogSNet) model that accounts for cognitive aspects of social perception. The model explicitly represents each social interaction as a trace in human memory with its corresponding dynamics. The strength of the trace is the only measure of the influence that the interactions had on a person. For validation, we apply our model to NetSense data on social interactions among university students. The results show that CogSNet significantly improves the quality of modeling of human interactions in social networks.