  A protein residue network (PRN) is a network of interacting amino acids
within a protein. We describe characteristics of a sparser, highly central and
more volatile sub-network of a PRN called the short-cut network (SCN), as a
protein folds under molecular dynamics (MD) simulation with the goal of
understanding how proteins form navigable small-world networks within
themselves. The edges of an SCN are found via a local greedy search on a PRN.
SCNs grow in size and transitivity strength as a protein folds, and SCNs from
successful MD trajectories are better formed in these terms. Findings from an
investigation on how to model the formation of SCNs using dynamic graph theory,
and suggestions to move forward are presented. A SCN is enriched with
short-range contacts and its formation correlates positively with secondary
structure formation. Thus our approach to modeling PRN formation, in essence
protein folding from a graph theoretic view point, is more in tune with the
notion of increasing order to a random graph than the other way around, and
this increase in order coincides with improved navigability of PRNs.
