  Many physical and biological systems can be studied using complex network
theory, a new statistical physics understanding of graph theory. The recent
application of complex network theory to the study of functional brain networks
generated great enthusiasm as it allows addressing hitherto non-standard issues
in the field, such as efficiency of brain functioning or vulnerability to
damage. However, in spite of its high degree of generality, the theory was
originally designed to describe systems profoundly different from the brain. We
discuss some important caveats in the wholesale application of existing tools
and concepts to a field they were not originally designed to describe. At the
same time, we argue that complex network theory has not yet been taken full
advantage of, as many of its important aspects are yet to make their appearance
in the neuroscience literature. Finally, we propose that, rather than simply
borrowing from an existing theory, functional neural networks can inspire a
fundamental reformulation of complex network theory, to account for its
exquisitely complex functioning mode.
