Protein-protein interaction (PPI) networks have been used to investigate the influence of SARS-CoV-2 viral proteins on the function of human cells, laying out a deeper understanding of COVID--19 and providing ground for drug repurposing strategies. However, our knowledge of (dis)similarities between this one and other viral agents is still very limited. Here we compare the novel coronavirus PPI network against 45 known viruses, from the perspective of statistical physics. Our results show that classic analysis such as percolation is not sensitive to the distinguishing features of viruses, whereas the analysis of biochemical spreading patterns allows us to meaningfully categorize the viruses and quantitatively compare their impact on human proteins. Remarkably, when Gibbsian-like density matrices are used to represent each system's state, the corresponding macroscopic statistical properties measured by the spectral entropy reveals the existence of clusters of viruses at multiple scales. Overall, our results indicate that SARS-CoV-2 exhibits similarities to viruses like SARS-CoV and Influenza A at small scales, while at larger scales it exhibits more similarities to viruses such as HIV1 and HTLV1.