  Biomolecular networks have already found great utility in characterizing
complex biological systems arising from pair-wise interactions amongst
biomolecules. Here, we review how graph theoretical approaches can be applied
not only for a better understanding of various proximate (mechanistic)
relations, but also, ultimate (evolutionary) structures encoded in such
networks. A central question deals with the evolutionary dynamics by which
different topologies of biomolecular networks might have evolved, as well as
the biological principles that can be hypothesized from a deeper understanding
of the induced network dynamics. We emphasize the role of gene duplication in
terms of signaling game theory, whereby sender and receiver gene players accrue
benefit from gene duplication, leading to a preferential attachment mode of
network growth. Information asymmetry between sender and receiver genes is
hypothesized as a key driver of the resulting network topology. The study of
the resulting dynamics suggests many mathematical/computational problems, the
majority of which are intractable but yield to efficient approximation
algorithms, when studied through an algebraic graph theoretic lens.
