  Over the last few years, several computational techniques have been devised
to recover protein complexes from the protein interaction (PPI) networks of
organisms. These techniques model "dense" subnetworks within PPI networks as
complexes. However, our comprehensive evaluations revealed that these
techniques fail to reconstruct many 'gold standard' complexes that are "sparse"
in the networks (only 71 recovered out of 123 known yeast complexes embedded in
a network of 9704 interactions among 1622 proteins). In this work, we propose a
novel index called Component-Edge (CE) score to quantitatively measure the
notion of "complex derivability" from PPI networks. Using this index, we
theoretically categorize complexes as "sparse" or "dense" with respect to a
given network. We then devise an algorithm SPARC that selectively employs
functional interactions to improve the CE scores of predicted complexes, and
thereby elevates many of the "sparse" complexes to "dense". This empowers
existing methods to detect these "sparse" complexes. We demonstrate that our
approach is effective in reconstructing significantly many complexes missed
previously (104 recovered out of the 123 known complexes or ~47% improvement).
