This thesis investigates the computational performance of neural networks (NNs) in addressing a challenging problem known as the planted clique problem. This is a highly significant problem in average-case complexity theory due to its large statistical-computational gap. The primary aim of this thesis is to conduct a numerical analysis of NNs, comparing them with existing algorithms, and exploring potential similarities in problem-solving strategies employed by NNs and humans. Firstly, the problem's setting is introduced, focusing on the detection of graphs with planted cliques. Different algorithms used to solve this task are described, among which Approximate Message Passing (AMP) is identified as the best known algorithm.