  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.
