We are living in a world which is getting more and more interconnected and, as physiological effect, the interaction between the entities produces more and more information. This high throughput generation calls for techniques able to reduce the volume of the data, but still able to preserve the carried knowledge. Data compression and summarization techniques are one of the possible approaches to face such problems. The aim of this thesis is to devise a new pipeline for compressing and decompressing a graph by exploiting Szemerédi's Regularity Lemma. In particular, it has been developed a procedure called CoDec (Compression-Decompression) which is based on Alon et al's constructive version of the Regularity Lemma. We provide an extensive experimental evaluation to measure how robust is the framework as we both corrupt the structures carried by the graph and add noisy edges among them. The experimental results make us confident that our method can be effectively used as a graph compression technique able to preserve meaningful patterns of the original graph.