How often are complex networks and graph theory useful in computational neuroscience?

Question

Complex networks and graph theory seem like they would be important for computational neuroscience, but they don't come up in the literature as often as I would expect. I'm wondering how frequently they are utilized and what specific ways they tend to be applied.

Answer 1

In my opinion as a computational neuroscience researcher, graph theory has not made major inroads into computational neuroscience because we don't have good evidence for what graphs characterise brains.

For example, my research revolves around how patterns of connections between neurons within local cortical circuits relate to information processing mechanisms performed by those circuits. But it's only very recently (e.g. Ko et al. 2011, Cossell et al. 2015, Markram et al. 2015, Lee et al. 2016) that we have detailed experimental data to build a connection graph on a very small scale.

The "small-world" concept was highly influential in neuroscience for a few years, but it turns out that "small-world" doesn't tell you anything much about the computations performed by a network, or even tell you anything much about it's detailed structure.

The work of Sporns (2004) and others have been applied to large-scale experimental data characterising connections between cortical areas. But again, the network motifs that come out from these experimental data sets statistically don't tell us much about what is going on computationally, or even how these areas connect to each other on a fine scale. The problem here is one of physical resolution of the techniques used.

Some aspects of random matrix theory apply to the sorts of networks that we can build, simulating what we know about connections within the brain (e.g. Rajan & Abbott 2006, Muir & Mrsic-Flogel 2015). Much of random matrix theory doesn't apply however, since graphs of realistic networks are non-Hermitian and can be quite constrained.

Answer 2

Graph theory and complex networks are central to many works involving fMRI (1, 2), whole brain models (3, 4), protein interaction graphs (5, 6), and some EEG studies of consciousness (7, 8, 9). The problem is that neuroscience is a very wide field that emcompases many different specific questions, most of which are pointed at small features that dont envolve huge networks.