Graph theory has provided a new set of tools for helping us to understand signal processing networks in the brain (see “Other related blog posts” below for some earlier posts on graph theoretic based approaches). In particular, a field known as network theory or complex network theory, which is rooted in graph theory, has been helping to provide insight into the way circuits in the brain are wired and how those circuits contribute to brain function. The new review paper “Dissecting functional connectivity of neuronal microcircuits: experimental and theoretical insights” (published online April 2, 2011 in Trends in Neuroscience) provides a high-level look at using network theory in the brain sciences.
First the authors explain key definitions for those unfamiliar with network theory. They discuss the features of networks that are typically captured in network theoretic equations. These equations are used for analyzing graphs composed of nodes and edges (links). Results of the analyses provide insights into the physical and functional organization of graphs.
The nature of the insights provided by the analysis of a graph depend on the graph’s composition. Nodes may represent any number of brain structures. For example, nodes may represent neurons, brain areas, or dendritic spines. Edges represent the means of communication amongst the structures represented by the nodes. For example, edges may represent chemical synapses, gap junctions, or diffusible molecules.
In network theory some general organizational principles have emerged. For instance, a scale-free network is a graph containing nodes that exhibit a wide range in their number of connections with other nodes. These graphs include rare hub nodes that have an extraordinarily large number of connections with other nodes. Hub nodes have a strong impact on signal processing within a network.
Scale-free networks are found in neuronal circuits in the brain. For example, an important structure for learning and memory known as the hippocampus exhibits scale-free network organization during development. The inhibitory GABAergic neurons in this structure act as hubs that help orchestrate synchronous activity across the network. If these concepts or their application in the brain sciences are interesting and new to you then you may find this review paper to be a good introduction.
Other related blog posts: