Mapping Brain Connectivity Using Graph Theory

Have you ever wondered why the same brain regions are often implicated again and again in many tasks and behaviors?  For instance, the prefrontal cortex is implicated in so many cognitive tasks that citing its involvement, per se, is hardly more illuminating or meaningful than throwing up one’s hands and saying, “It happened in the brain!”  Unfortunately, a contemporary pop-neuropsychology of brain “hotspots” and “centers” was born of the functional brain imaging of the ‘90s.  A casual reader of popular science would be lead to believe that the brain enjoys a functionally segregated architecture with highly differentiated modules for every conceivable task and function.  This oversimplified concept of brain function is akin to the pseudoscience of phrenology, a 19th century school of thought asserting that bumps on the skull indicate and determine skills and personality traits.

L0000992 Phrenology: Chart

One reason why this functional segregationist view of the brain has survived in popular science and even academic circles is because it is partially correct.  The neocortex strikes a fine balance between functional segregation and integration, a balance which is believed to be critical for consciousness and higher cognition.  Ignoring this balance often leads to poorly designed brain imaging experiments, lending misplaced significance to the unsurprising activation of brain regions without actually shedding light on how different brain regions interact to perform a function.

A more meaningful approach to studying functional brain activity is to characterize networks of brain regions from their correlated activity during a mental or behavioral task.  Understanding the brain as a network recognizes the balance between functional segregation and integration, while allowing for meaningful functional brain mapping.  A functional brain network is discovered by characterizing the correlated activity of distributed brain regions using the mathematical tools of graph theory.

Graph theory was born when the 18th century mathematician Leonhard Euler solved a contemporary problem asking if one could take a walk through the Prussian city of Königsberg without crossing any of its seven bridges more than once.  By quantitatively describing the connectivity of isolated city districts, Euler invented the first graph.  This is not the type of graph used to plot one variable against another, but rather a “map” describing a set of nodes (e.g., city districts, brain regions) connected by edges (e.g. bridges, white matter fibers).  Perhaps it is not entirely coincidence that a mathematical field originally invented to solve a navigational problem is today used to characterize the brain.  The connectivity of place cells in the hippocampus—each of which explicitly encodes a location in physical space—is used by the brain to navigate its environment.  The shortest path between two locations can be computed by tracing connections between place cells.  This is an example of a structural brain network, in which nodes are defined by anatomical connections rather than statistical relationships.  Structural brain networks are the physical substrate which gives rise to functional brain networks.

The mathematician Leonhard Euler developed the field of graph theory by showing that one cannot take a walk through the Prussian city of Konigsberg without crossing one of seven bridges connecting districts at least twice.

Many important functional brain networks have been characterized in recent years using graph theory.  Arguably the most notable is the default mode network (DMN), a set of hub nodes whose activity is highly correlated during cognitive rest.  Hubs are nodes in a graph with many neighbors, like city airports connecting flights to smaller and relatively isolated towns.  In the brain, the medial prefrontal cortex, medial temporal lobes, posterior cingulate cortex, and the precuneus form import hub nodes in the DMN.  Hubs nodes of frequently activated networks are not uniquely activated by one specific task.  Next time you hear a media report about a brain region activated by a specific task, ask yourself whether that brain region could also be part of a larger network responsible for many other tasks.

Functional magnetic resonance imaging (fMRI) is used to reveal correlated metabolic activity from brain regions constituting the Default Mode Network (DMN).



Images from Wikimedia Commons and made by Jooyeun Lee.

Joel Frohlich

Joel Frohlich is a postdoc studying consciousness in the lab of Martin Monti at UCLA. He is interested in using brain activity recorded with EEG to infer when a person is conscious. Joel earned his PhD from UCLA in 2018 studying EEG markers of neurodevelopmental disorders in the lab of Shafali Jeste. You can also check out Joel's blog Consciousness, Self-Organization, and Neuroscience on Psychology Today. For more about Joel's research and writing, please visit Joel's website at