The analysis of protein behavior at the network level had been applied to elucidate the mechanisms of protein interaction that are similar in different species. Published network alignment algorithms proved to be able to recapitulate known conserved modules and protein complexes, and infer new conserved interactions confirmed by wet lab experiments. In the meantime, however, a plethora of continuously evolving protein-protein interaction (PPI) data sets have been developed, each featuring different levels of completeness and reliability. For instance, algorithms performance may vary significantly when changing the data set used in their assessment. Moreover, existing papers did not deeply investigate the robustness of alignment algorithms. For instance, some algorithms performances vary significantly when changing the data set used in their assessment. In this work, we design an extensive assessment of current algorithms discussing the robustness of the results on the basis of input networks. We also present AlignMCL, a local network alignment algorithm based on an improved model of alignment graph and Markov Clustering. AlignMCL performs better than other state-of-the-art local alignment algorithms over different updated data sets. In addition, AlignMCL features high levels of robustness, producing similar results regardless the selected data set.