Several studies have been carried out on the graph matching problem, which is a generalization of the classic graph isomorphism problem. A graph-matching algorithm finds a map between the vertex sets of two similar graphs with only information about their topological structure. This has applications in many fields, especially in the deanonymization of social and information networks, which can be represented through graphs. It’s rather clear, from the whole body of work, that anonymizing node identities is not sufficient to guarantee privacy protection and can be overcome. In this thesis, the Percolation Graph Matching (PGM) algorithm is considered, a very simple algorithm, based on bootstrap percolation.