  Proteins are essential macromolecules of life and thus understanding their
function is of great importance. The number of functionally unclassified
proteins is large even for simple and well studied organisms such as baker's
yeast. Methods for determining protein function have shifted their focus from
targeting specific proteins based solely on sequence homology to analyses of
the entire proteome based on protein-protein interaction (PPI) networks. Since
proteins aggregate to perform a certain function, analyzing structural
properties of PPI networks may provide useful clues about the biological
function of individual proteins, protein complexes they participate in, and
even larger subcellular machines.
  We design a sensitive graph theoretic method for comparing local structures
of node neighborhoods that demonstrates that in PPI networks, biological
function of a node and its local network structure are closely related. The
method groups topologically similar proteins under this measure in a PPI
network and shows that these protein groups belong to the same protein
complexes, perform the same biological functions, are localized in the same
subcellular compartments, and have the same tissue expressions. Moreover, we
apply our technique on a proteome-scale network data and infer biological
function of yet unclassified proteins demonstrating that our method can provide
valuable guidelines for future experimental research.
