Reconstructing functional brain networks: have we got the basics right?

Both at rest and during the executions of
\ncognitive tasks, the brain continuously creates
\nand reshapes complex patterns of correlated
\ndynamics. Thus, brain functional
\nactivity is naturally described in terms of
\nnetworks, i.e., sets of nodes, representing
\ndistinct subsystems, and links connecting
\nnode pairs, representing relationships
\nbetween them.
\nRecently, brain function has started
\nbeing investigated using a statistical
\nphysics understanding of graph theory,
\nan old branch of pure mathematics
\n(Newman, 2010). Within this framework,
\nnetwork properties are independent of the
\nidentity of their nodes, as they emerge
\nin a non-trivial way from their interactions.
\nObserved topologies are instances
\nof a network ensemble, falling into one of
\nfew universality classes and are therefore
\ninherently statistical in nature.
\nFunctional network reconstruction
\ncomprises various steps: first, nodes are
\nidentified; then, links are established
\naccording to a certain metric. This gives
\nrise to a clique with an all-to-all connectivity.
\nDeciding which links are significant
\nis done by choosing which values of these
\nmetrics should be taken into account.
\nFinally, network properties are computed
\nand used to characterize the network.
\nEach of these steps contains an element
\nof arbitrariness, as graph theory
\nallows characterizing systems once a network
\nis reconstructed, but is neutral as
\nto what should be treated as a system
\nand to how to isolate its constituent
\nparts.
\nHere we discuss some aspects related
\nto the way nodes, links and networks in
\ngeneral are defined in system-level studies
\nusing noninvasive techniques, which may
\nbe critical when interpreting the results of
\nfunctional brain network analyses.