Humans are often involved in complex social relationships, where they exhibit biased behavior when they process information from neighbors (e.g., irrational DeGroot learning) and cognitive biases on perceiving social network structures (e.g., egocentric biases, network centrality, etc.). But little is known about the cognitive reason behind. Here we purpose a unified computational framework (reduced representation model, RRM) to deal with the problems, which assumes people represent an optimal reduced network based on the trade-off of utility and cognitive cost for the representation, and make rational inference on it, where DeGroot-like behavior emerges. We did simulations to show RRM can provide an underlying explanation for DeGroot model and human perceptual biases, and tested model predictions in previous dataset (n=209), lab experiment (n=248) and field data. Our work provides an optimal way to depict social network representation when considering human cognitive limitations, and may help understand widespread human biases in social environments.