Upon reading the article, I learned that it is possible to map the functions of the brain using graph theory. Vanderbilt University researchers used vertices to correspond to parts of the brain and edges to map the communication between each of the parts. 24 subjects were experimented upon, in which they were each given an fMRI  and asked to detect a disk on the screen and how much confidence they had in their answer. These results were then measured and graphed. No single part of the brain stood out in any way, as predicted by researchers. A few parts of the brain had more vertices than others. This suggests that consciousness is part of widespread communication throughout the brain and there is no one part controls most functions.
I find this application of graph theory to be interesting and innovative to help further understand what science knows about the brain. I was surprised to find graph theory applied in this way.

Source: http://news.vanderbilt.edu/2015/03/213466/