Nodes and edges
Last Thursday, one of Albert-László Barabási‘s post doctoral researchers, Yang Yu Liu, co-authored a News & Views article for Nature Physics. Together with MIT’s Jean-Jacques Slotine, Liu summarizes the impact of a research article published online that same day. The research was carried out by Barabási’s colleagues at the Hungarian Academy of Sciences in Budapest and looks at controlling complex networks in an altogether new way.
Instead of focusing on controlling the “nodes” in a complex network they care more about how to control the “edges.” In a social network, the nodes are all the individuals and the edges are the information they share with one another — the stuff that gets passed along their connection.
On a map of the United States the nodes might be the cities and the edges the streets that connect them. It occurred to me as I was reading the article that the new methodology is like the map that emerges when you only draw out the streets:
rather than the map that emerges when you only draw out the cities:
Looking at the streets can actually give you more information than just looking at the population density. Here’s a close up of the Appalachian Mountain area of Ben Fry’s All Streets map:
But still, in the case of a US map, you do get the same general picture. The outline of the map keeps it shape. Cities show up in the All Streets map because there are more people and thus more streets to move them around on.
But what if the nodes and edges weren’t so proportionate to one another? In the case of the human brain, where the nodes are neurons and the edges are electrical connections between them, there are about 10 million times as many nodes as there are edges. That means that looking at the nodes might give an incredibly different kind of picture than looking at the edges in this particular case.
I guess people have shied away from this sort of approach because edges can be rather amorphous — “after all, the edges of complex networks may not even be physical entities,” say Liu and Slotine. But in many cases, even if the edge isn’t a physical entity, looking at the system in this way can give a more accurate picture.
So why do they even care? Why do they want to know what a system looks like and how to “control” it? What does it even mean to “control” a system? Barabási explained it to me through the analogy of driving a car. An automobile is made up of thousands of interconnected parts, but all we have to do to control it is turn the wheel, press the pedals and shift the gears (if you’re old school). These are the nodes. Imagine if we didn’t know what they were or how they worked with the rest of the system. We might spend a lifetime trying to figure out how to drive a car.
Network science works in reverse. Whereas the network of parts in a car is specifically engineered to be controlled by humans, most networks we encounter are not: the social network, the network of cells in the human body, the neuronal network in the brain. Developing new drug therapies and predicting the spread of disease are dependent upon a comprehensive understanding of the system at hand. Controlling the system could even prevent catastrophe in some cases. But in order to understand it, you need to tease out the relevant information.
The edge-centered approach may enhance that process.