We study individual ability to memorize and recall information about friendship networks using a combination of experiments and survey-based data. In the experiment subjects are shown a network, in which their location is exogenously assigned, and they are then asked questions about the network after it disappears. We find that subjects exhibit three main cognitive biases: (i) they underestimate the mean degree compared to the actual network; (ii) they overestimate the number of rare degrees; (iii) they underestimate the number of frequent degrees. We then analyse survey data from two `real' friendship networks from a Silicon Valley firm and from a University Research Center. We find, somewhat remarkably, that individuals in these real networks also exhibit these biases. The experiments yield three further: findings: (iv) network cognition is a affected by the subject's location, (v) the accuracy of network cognition varies with the nature of the network, and (vi) network cognition has a significant effect on economic decisions.