Neural network pruning plays a crucial role in bringing recent artificial intelligence technologies to edge devices. Typically, when pruning a network, re-learning of previously learned samples is necessary to minimize the remaining error caused by the pruning process. However, there are scenarios where pruning must be performed without any available samples. While some pruning algorithms exist that do not rely on samples, most of them evaluate the importance of each weight parameter based on individual unit weights. Unfortunately, this approach often leads to incomplete evaluation results. In our proposed method, we take a different approach. By using a recurrent neural network known as the Fast and Deep Graph Neural Network (FDGNN), the embedding representations of hidden units are calculated based on the signal propagation pathways, and their norms are compared to estimate similarity. Compression is then performed by merging the most similar units. Let us denote the proposed method as PBRNN (pruning method by RNN). PBRNN was applied to AlexNet, the decrease in recognition accuracy was limited to 3.5% for Top-1 accuracy and 2.3% for Top-5 accuracy, representing an improvement of 10.4% and 8.239%, respectively, over existing methods.