## A (brief) introduction to Executive networksDr. William R. McCumber

Networks are everywhere. Electric grids. Highways. Food chains. The entire Internet. Much of my work concerns networks of executives, specifically, networks of people who serve on boards of directors of companies, non-profit entities, and government agencies. That's a lot of people, and that means big data analytics, supercomputers, and finance. My kind of geek paradise.

In network (graph) terminology, a NODE is an entity, in this case, an executive, and a LINK or EDGE is a relationship between nodes. Nodes are typically represented as dots, and links as lines between nodes. For our purposes here, two executives are "linked" if they sit on the same board at the same time. Here's a small example network of 11 nodes and 20 edges:

small sample network

In financial network literature, the most common measure of a node's network "importance" is DEGREE CENTRALITY, which is the number of direct connections an executive has with other executives. In other words, degree centrality is the size of one's immediate network.

It looks like Bob is a pretty important guy. He has the highest degree centrality because he is directly connected to 10 other nodes.

A related concept is that of EIGENVECTOR CENTRALITY, which is degree centrality weighted by the degree centralities of one's direct connections. Eigenvector centrality measures how "connected" your connections are; you have higher eigenvector centrality if your connections are also influential. Bob wins again, because he connected to almost all other nodes, which are in turn connected to others in the network.

Now look at nodes "a", "b", and "Jun". Each has a degree centrality of 1, because they are connected to only one other node. But Jun has higher eigenvector centrality because he is connected to Bob, whom, let's face it, is kind of a big deal.

You may have heard of "six degrees of separation" or, it's cute but cool derivative, "Six degrees of Kevin Bacon". Apologies to Mr. Bacon, but this roughly demonstrates the idea behind CLOSENESS CENTRALITY, which is a spatial representation of an executive's network position. Closeness centrality is the inverse of the distance - the number of steps it takes to reach - all other executives in the network. Under the assumption that distance both erodes the accuracy of information and makes it more costly to obtain, an executive is advantageously positioned if she enjoys higher closeness centrality.

Finally, we have BETWEENNESS CENTRALITY, another spatial representation of executive network position. Betweenness measures the frequency with which one is "between" two other executives. Betweeness is related to the concept of brokerage. In the example to the left, B has the power to pass along, alter, or block information from A to C and vice versa. B would have a betweenness centrality of 1, because he is an information conduit between A and C 100% of the time. Sadly, A and C would have a betweenness centrality of 0.

Here's a representation of a small sub network of the global executive network. This is a snapshot of a network of North American banking executives in 2004. Actually, it's a sub network of the sub network, because only "average" bankers are represented here, those with degree centralities in the middle 50% of the distribution of all banker degree centralities that year. That still includes 16,663 banking directors, their connections to 61,851 other executives, and the 1,618,142 direct connections between them all. People are dots. The size of the dot is scaled by degree centrality (bigger dots are more connected people). Colored lines between nodes are the links or edges - the relationships - between them. Since this is about bank directors, 77% of all links are bank boards, in purple. But you can also see specialty finance (green), software (blue), telecommunications (brown), and more.

Note the tight clusters of relationships. Also note the periphery players, those with only one (or a few) links to the network.

Taking a deep dive into the center of the bank director sub network looks like a thick web. Which it is. If you believe that networks are part of the infrastructure enabling information flows (because firms don't talk - people talk), then it's easier to visualize information flows when you actually can SEE a network.

Here again you can see people (black circles), the relative size of their networks (bigger circles designates their immediate influence or network importance), tight clusters of executives, and the links between them. Hey, it looks like we found a vein of biotech relationships running through the center here - the tight band of pink/red edges. Pretty cool.

Okay, last one for now. This is a close up - in the Canadian large cluster - of a sub network of Canadian executives (pink-ish) and Malaysian executives (green) and the board relationships between them, in 2013. There are 2,171 Canadians, 1,845 Malaysians, 71,946 other executives linked to the Canadian and Malaysian folks, who together have 246,220 links between them. Again, dots are people, the size of the dots varies by how "connected" these people are, and lines represent relationships. You can see tight clusters of relatively unconnected people, large nodes (very connected executives) tied to these clusters, and more.

Networks can be "good", in that they promote more efficient information flows, enable trust transactions, and are the conduit through which reputations are enhanced or damaged. In this way, network studies are also studies of social capital, trust, and reputation in addition to information flows.

Networks can also be "bad" if they insulate bad actors from discipline, allow black markets to flourish, or otherwise enable "sub optimal" behaviors.

There are several studies that show these good/bad network effects in economics and finance - political connections and payouts (bad), governance propagation across director networks (good), value-destroying acquisitions and entrenched CEOs (bad), lower cost of debt capital for firms with more connected managers (good), profitable informed trading when directors are more connected (bad), greater liquidity when executives are more connected (good), and the list goes on.

That said, it's an exciting time to be in networks research because there are still so many unanswered questions. The constraint on this research is not the number of questions to explore, but computing power. We are on the very edge of big-data analytics using even the most powerful supercomputers - and we're having a great time doing it.

Finally, I should wrap up this very brief introduction with an acknowledgement. The small example network figure and the "banker network" figures are from "Executive Network Centrality and Stock Liquidity", forthcoming in Financial Management, that I co-authored with Dr. Jared Egginton. The Canadian and Malaysian close up is from a working paper on global networks and liquidity, co-authored with professors Dr. Garrett McBrayer and Dr. Jared Egginton.

Should you need to reach me, I am best found at mccumber[at]latech.edu.

Credits:

Created with images by geralt - "system web network" • geralt - "network earth block chain"