Nodes and edges

Okay readers, be pre­pared for a cir­cuitous walk down Net­work Lane today.

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:

You can actu­ally see the topog­raphy begin to emerge where there are no streets — looking at the edges reveals some­thing about the map that looking at the nodes does not.

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.

Images: “All Streets Map,” via Fathom Infor­ma­tion Design; “US at Night Showing Low and High Den­sity,” via Georgia Info