Networks, as efficient representations of complex systems, have appealed to
scientists for a long time and now permeate many areas of science, including
neuroimaging (Bullmore and Sporns 2009 Nat. Rev. Neurosci. 10, 186–198.
(doi:10.1038/nrn2618)). Traditionally, the structure of complex networks has
been studied through their statistical properties and metrics concerned with
node and link properties, e.g. degree-distribution, node centrality and modularity.
Here, we study the characteristics of functional brain networks at the
mesoscopic level from a novel perspective that highlights the role of inhomogeneities
in the fabric of functional connections. This can be done by focusing
on the features of a set of topological objects—homological cycles—associated
with the weighted functional network. We leverage the detected topological
information to define the homological scaffolds, a new set of objects designed to
represent compactly the homological features of the correlation network and
simultaneously make their homological properties amenable to networks theoretical
methods. As a proof of principle, we apply these tools to compare restingstate
functional brain activity in 15 healthy volunteers after intravenous infusion
of placebo and psilocybin—the main psychoactive component of magic mushrooms.
The results show that the homological structure of the brain’s functional
patterns undergoes a dramatic change post-psilocybin, characterized by the
appearance of many transient structures of low stability and of a small
number of persistent ones that are not observed in the case of placebo.