While protesters are trying to occupy Wall Street and spread their movement to other cities…
… others are trying to mathematically analyze the network of global corporate control:
• Stefania Vitali, James B. Glattfelder and Stefano Battiston, The network of global corporate control.
Here’s a little ‘directed graph':
Very roughly, a directed graph consists of some vertices and some edges with arrows on them. Vitali, Glattfelder and Battiston built an enormous directed graph by taking 43,060 transnational corporations and seeing who owns a stake in whom:
If we zoom in on the financial sector, we can see the companies those protestors are upset about:
Zooming out again, we could check that the graph as a whole consists of many pieces. But the largest piece contains 3/4 of all the corporations studied, including all the top by economic value, and accounting for 94.2% of the total operating revenue.
Within this there is a large ‘core’, containing 1347 corporations each of whom owns directly and/or indirectly shares in every other member of the core. On average, each member of the core has direct ties to 20 others. As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. As the authors put it:
This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.
If you’ve never thought much about modern global capitalism, the existence of this ‘core’ may seem shocking and scary… like an enormous invisible spiderweb wrapping around the globe, dominating us, controlling every move we make. Or maybe you can see a tremendous new business opportunity, waiting to be exploited!
But if you’ve already thought about these things, the existence of this core probably seems obvious. What’s new here is the use of certain ideas in math—graph theory, to be precise—to study it quantitatively.
So, let me say a bit more about the math! What’s a directed graph, exactly? It’s a set and a subset of . We call the elements of vertices and the elements of edges. Since an edge is an ordered pair of vertices, it has a ‘starting point’ and an ‘endpoint’—that’s why we call this kind of graph ‘directed’.
(Note that we can have an edge going from a vertex to itself, but we cannot have more than one edge going from some vertex to some vertex . If you don’t like this, use some other kind of graph: there are many kinds!)
I spoke about ‘pieces’ of a directed graph, but that’s not a precise term, since there are various kinds of pieces:
• A connected component is a maximal set of vertices such that we can get from any one to any other by an undirected path, meaning a path of edges where we don’t care which way the arrows point.
• A strongly connected component is a maximal set of vertices such that we can get from any one to any other by an directed path, meaning a path of edges where at each step we walk ‘forwards’, along with the arrow.
I didn’t state these definitions very precisely, but I hope you can fill in the details. Maybe an example will help! This graph has three strongly connected components, shaded in blue, but just one connected component:
So when I said this:
The graph consists of many pieces, but the largest contains 3/4 of all the corporations studied, including all the top by economic value, and accounting for 94.2% of the total operating revenue.
I was really talking about the largest connected component. But when I said this:
Within this there is a large ‘core’ containing 1347 corporations each of whom owns directly and/or indirectly shares in every other member of the core.
I was really talking about a strongly connected component. When you look at random directed graphs, there often turns out to be one strongly connected component that’s a lot bigger than all the rest. This is called the core, or the giant strongly connected component.
In fact there’s a whole study of random directed graphs, which is relevant not only to corporations, but also to webpages! Webpages link to other webpages, giving a directed graph. (True, one webpage can link to another more than once, but we can either ignore that subtlety or use a different concept of graph that handles this.)
And it turns out that for various types of random directed graphs, we tend to get a so-called ‘bowtie structure’, like this:
In the middle you see the core, or giant strongly connected component, labelled SCC. (Yes, that’s where Exxon sits, like a spider in the middle of the web!)
Connected to this by paths going in, we have the left half of the bowtie, labelled IN. Connected to the core by paths going out, we have the right half of the bowtie, labelled OUT
There are also usually some IN-tendrils going out of the IN region, and some OUT-tendrils going into the ‘OUT’ region.
There may also be tubes going from IN to OUT while avoiding the core.
All this is one connected component: the largest one. But finally, not shown here, there may be a bunch of other smaller connected components. Presumably if these are large enough they have a similar structure.
Now: can we use this knowledge to do something good? Or it all too obvious so far? After all, so far we’re just saying the network of global corporate control is a fairly ordinary sort of random directed graph. Maybe we need to go beyond this, and think about ways in which it’s not ordinary. In fact, I should reread the paper with that in mind.
Or… well, maybe you have some ideas.
(By the way, I don’t think ‘overthrowing’ the network of global corporate control is a feasible or even desirable project. I’m not espousing any sort of revolutionary ideology, and I’m not interested in discussing politics here. I’m more interested in understanding the world and looking for some leverage points where we can gently nudge things in slightly better directions. If there were a way to do this by taking advantage of the power of corporations, that would be cool.)