<p>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.</p>

<p>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. <a href="https://doi.org/10.1038/nature09880" rel="noreferrer" title="Ko et al. 2011">Ko et al. 2011</a>, <a href="https://doi.org/10.1038/nature14182" rel="noreferrer" title="Cossell et al. 2015">Cossell et al. 2015</a>, <a href="https://doi.org/10.1016/j.cell.2015.09.029" rel="noreferrer" title="Markram et al. 2015">Markram et al. 2015</a>, <a href="https://doi.org/10.1038/nature17192" rel="noreferrer" title="Lee et al. 2016">Lee et al. 2016</a>) that we have detailed experimental data to build a connection graph on a very small scale.</p>

<p>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.</p>

<p>The work of Sporns (<a href="https://doi.org/10.1371/journal.pbio.0020369" rel="noreferrer" title="Sporns &amp; Kotter 2004">2004</a>) 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.</p>

<p>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. <a href="https://doi.org/10.1103/PhysRevLett.97.188104" rel="noreferrer" title="Rajan &amp; Abbott 2006">Rajan &amp; Abbott 2006</a>, <a href="https://doi.org/10.1103/PhysRevE.91.042808" rel="noreferrer" title="Muir &amp; Mrsic-Flogel 2015">Muir &amp; Mrsic-Flogel 2015</a>). Much of random matrix theory doesn't apply however, since graphs of realistic networks are non-Hermitian and can be quite constrained.</p>

CC BY-SA 3.0
2017-04-19T16:22:54.080Z
2017-04-19T16:22:54.080Z
Dylan Richard Muir
<p>Graph theory and complex networks are central to many works involving fMRI (<a href="http://www.pnas.org/cgi/doi/10.1073/pnas.1106612109" rel="nofollow noreferrer">1</a>, <a href="http://www.pnas.org/content/103/37/13848.full" rel="nofollow noreferrer">2</a>), whole brain models (<a href="http://dx.plos.org/10.1371/journal.pcbi.1005025" rel="nofollow noreferrer">3</a>, <a href="http://www.nature.com/doifinder/10.1038/nn.3690" rel="nofollow noreferrer">4</a>), protein interaction graphs (<a href="http://science.sciencemag.org/content/296/5569/910" rel="nofollow noreferrer">5</a>, <a href="http://www.nature.com/nature/journal/v411/n6833/abs/411041a0.html" rel="nofollow noreferrer">6</a>), and some EEG studies of consciousness (<a href="http://www.pnas.org/content/112/3/887.full" rel="nofollow noreferrer">7</a>, <a href="http://cercor.oxfordjournals.org/content/25/11/4203.full" rel="nofollow noreferrer">8</a>, <a href="http://brain.oxfordjournals.org/content/133/1/161.short" rel="nofollow noreferrer">9</a>). 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.</p>

CC BY-SA 3.0
2017-01-09T13:00:02.670Z
could you add some sources to your answer to allow other users to background read on your answer?
AliceD
CC BY-SA 3.0
2017-01-09T13:01:41.843Z
Yes, Im on my cell now. When I get to my PC Ill add sources to my answer
lucianopaz
CC BY-SA 3.0
2017-01-09T12:46:24.690Z
2017-01-09T15:06:43.823Z
2017-01-09T15:06:43.823Z
lucianopaz
<p>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.</p>

CC BY-SA 3.0
2016-12-01T00:13:03.420Z
Not sure about computational neuroscience specifically, but graph theory is used all the time in general neuroscience for brain network stuff (see Olaf Sporns, Martijn van den Heuvel, etc.).
mrt
CC BY-SA 3.0
2016-12-04T01:11:40.263Z
Ahh, yes thanks. I've started reading some stuff by Sporns, though I haven't gotten to the part where "it all comes together" as of yet.
Logan Collins
<cognitive-neuroscience><cognitive-modeling><computational-modeling><mathematical-psychology>
How often are complex networks and graph theory useful in computational neuroscience?
Logan Collins
# How often are complex networks and graph theory useful in computational neuroscience?

(Asked by: username_0 on 2016-11-30)

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.

**Tags:** cognitive-neuroscience, cognitive-modeling, computational-modeling, mathematical-psychology

> **Comments:**
> **username_1**: Not sure about computational neuroscience specifically, but graph theory is used all the time in general neuroscience for brain network stuff (see Olaf Sporns, Martijn van den Heuvel, etc.).  
> **username_0**: Ahh, yes thanks. I've started reading some stuff by Sporns, though I haven't gotten to the part where "it all comes together" as of yet.  

---

## 2 answers

### Answer by username_2 on 2017-04-19. Score: 6

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](https://doi.org/10.1038/nature09880 "Ko et al. 2011"), [Cossell et al. 2015](https://doi.org/10.1038/nature14182 "Cossell et al. 2015"), [Markram et al. 2015](https://doi.org/10.1016/j.cell.2015.09.029 "Markram et al. 2015"), [Lee et al. 2016](https://doi.org/10.1038/nature17192 "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](https://doi.org/10.1371/journal.pbio.0020369 "Sporns & Kotter 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](https://doi.org/10.1103/PhysRevLett.97.188104 "Rajan & Abbott 2006"), [Muir & Mrsic-Flogel 2015](https://doi.org/10.1103/PhysRevE.91.042808 "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.


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### Answer by username_3 on 2017-01-09. Score: 1

Graph theory and complex networks are central to many works involving fMRI ([1](http://www.pnas.org/cgi/doi/10.1073/pnas.1106612109), [2](http://www.pnas.org/content/103/37/13848.full)), whole brain models ([3](http://dx.plos.org/10.1371/journal.pcbi.1005025), [4](http://www.nature.com/doifinder/10.1038/nn.3690)), protein interaction graphs ([5](http://science.sciencemag.org/content/296/5569/910), [6](http://www.nature.com/nature/journal/v411/n6833/abs/411041a0.html)), and some EEG studies of consciousness ([7](http://www.pnas.org/content/112/3/887.full), [8](http://cercor.oxfordjournals.org/content/25/11/4203.full), [9](http://brain.oxfordjournals.org/content/133/1/161.short)). 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.

> **Comments:**
> **username_4**: could you add some sources to your answer to allow other users to background read on your answer?  
> **username_3**: Yes, Im on my cell now. When I get to my PC Ill add sources to my answer  

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