Networks in the autistic brain: insights from graph theory

First published in Cracking the Enigma, December 2010

A couple of weeks ago I travelled from Sydney to a conference taking place in San Diego, California. There isn’t a direct flight to San Diego so instead I had to fly via Los Angeles. Colleagues coming from Melbourne had an even more convoluted journey – they had to get a connecting flight to Sydney first before they could fly to LA. Airline routes are determined by economic pressures. There simply aren’t enough people wanting to travel from Sydney or Melbourne to San Diego on a regular basis for a direct route to be commercially viable. Instead, travellers rely on a small number of long-distance routes with local connecting flights at either end. In this way, it’s still possible to get between any two airports with only a couple of flight transfers along the way.

It turns out that the brain operates according to similar network economics. Neurons communicate via action potentials – electric pulses sent along their axons. Ordinarily, these are quite slow, so in order to send messages quickly over long distances in the brain, axons have to be insulated by a fatty sheath known as myelin. However, it’s not feasible to have every axon heavily myelinated – for one thing, the myelinated axons would take up too much space in the brain. So, as with the airlines, there are lots of local connections within brain regions and a limited number of long-range super-fast myelinated connections. And as with the airlines, this actually allows messages to be sent across the brain relatively efficiently, with every neuron being only a few synapses (flight transfers) from every other neuron.

This is more than just an extended metaphor. In fact, there is an entire branch of mathematics, known as ‘graph theory’, that can be applied to pretty much every imaginable kind of network – from airports around the world to co-stars in Hollywood movies, or friendship ‘circles’ on Facebook.

Researchers have recently begun applying those same graph theory principles to human neuroimaging data. And now, in a new paper, currently in press at Neuropsychologia, Pablo Barttfeld and colleagues from Buenos Aires have applied graph theory to autism.

In Barttfeld et al.’s study, 10 adults with autism and 10 non-autistic adults were asked to look at a cross on a computer screen, while the electrical currents generated by their brains were measured via 128 EEG electrodes placed strategically in different locations on their scalps. The researchers then estimated the strength of the connection between each pair of electrodes. If two electrodes recorded similar changes in the EEG response across time, they were deemed to be strongly connected. Connections below a certain threshold were eliminated, leaving a network with only the stronger connections. The researchers then used graph theory to characterise the network of inter-electrode connections.

The main findings were as follows:

The brain networks for autistic adults were less interconnected than those for the control group. On average, each electrode had fewer neighbours to which it was connected. In our air travel analogy, this corresponds to there being fewer routes between different airports.

The path length was also longer. Path length refers to the minimum number of steps it takes to get from A to B. My journey from Sydney to San Diego via LA had a path length of two because there were two separate flights involved. My colleagues from Melbourne had a path length of three.

Finally, the autistic network was more modular – removing the weaker connections very quickly led to a sub-divided network where it was impossible to get from one region to another. The analogy would be a network where it was possible to fly around Australia or America but impossible to get between the two.

While the methods are new, the findings really just confirm much of what we already know about autism. There’s plenty of evidence from other studies that autistic brains are less well connected (or the connection patterns are different to typical brains). The exciting aspect of this paper is that it introduce a whole new way of thinking about the autistic brain.

In particular, thinking in terms of networks and graph theory might finally allow us to reconcile connectivity theories of autism with other theories that focus more on localised brain dysfunction. Over the years, it has been variously argued that autism is caused by dysfunction of the hippocampus, the cerebellum, the temporo-parietal junction, the medial prefrontal cortex, and the amygdala, to name just a few brain regions. What these regions have in common is that they are all highly connected with other brain regions – they are the Chicago O’Hares and London Heathrows of the brain. Dysfunction of any of these regions could have huge impacts on the whole of the brain (imagine the knock-on effects of closing Heathrow airport). Alternatively, changes in global connectivity would have greatest impact on the functioning of these hubs.

This approach may also help us get a better handle on genetic causes of autism and the overlap with other disorders. As mentioned in my previous post, some of the genes implicated in autism may be better conceived as genes for neural connectivity that act as risk factors for a range of disorders. Graph theory offers a potential way of quantifying these effects. Indeed, using a similar approach, Stam and colleagues have already shown that the network properties of EEG are highly heritable and are compromised in schizophrenia.


Pablo Barttfeld, Bruno Wicker, Sebastián Cukier, Silvana Navarta, Sergio Lew, & Mariano Sigman (2010). A big-world network in ASD: Dynamical connectivity analysis reflects a deficit in long-range connections and an excess of short-range connections Neuropsychologia arXiv: 1007.5471v1