When collecting covert network data, researchers prioritize finding edges without confirming the absence of a tie. This suggests value in research on the process of sampling edges. However, little research has been done in this area. We use the line graph and the auto-logistic actor attribute model to systematically formulate biased sampling processes to reflect realistic sampling biases. We define what might be termed person of interest (POI) bias in the model to reflect the dependence between sampled edges. We present a few examples using different population networks. We conclude that biased sampling processes can result in highly structured observed networks even when the population network lacks structure.