Large international corporations can control a wide variety of smaller companies. For example, Scientific American is a publication of Nature Publishing Group, which is a subsidiary of the Georg Von Holtzbrinck Publishing Group in Germany. This group also owns a number of other publishers in the U.S., United Kingdom, and Germany, a pyramid that includes American suspense thrillers, British textbooks, a German weekly newspaper and more. But corporate pyramids like that of the Von Holtzbrinck Publishing Group do not stand alone: The web of relationships among companies is tangled and complex, as a July 28 paper published to pre-print blog arXiv.org reveals.

A team of ETH Zurich (Swiss Federal Institute of Technology Zurich) researchers used a network model to map the ownership relations among more than 43,000 transnational corporations, which do not identify themselves with one country but rather use a global perspective and employ an international roster of executives. Owning shares in a company grants the owner some direct control of that entity, and indirect control of any companies in the parent-company's pyramid. By treating each major corporation as a node and drawing links between companies that owned shares of others, the researchers uncovered the tendrils of control that link one pyramid to another.

The links between nodes, shown above, represent influence that can flow two ways: any corporation could either influence or be influenced by any other corporation. Directly owning shares of a company gave a corporation more influence than indirect ownership, and the researchers assigned their links certain weights to reflect this difference. At first glance, the picture that emerged looks quite convoluted. However, the researchers discovered that the web of connections clustered into four different components that took the shape of a bow tie. In the illustration, red dots represent nodes, green arrows point from share-owner to the owned company, and the flow of control points in the direction of the most power.

The researchers observed a central cluster in which influence goes both ways between all the nodes, called the strongly connected component, or SCC, as shown above. Within the SCC, each member either directly or indirectly owns some of every other member's shares. Second, there was the in group, companies that owned shares in various members of the SCC, but were not under the SCC's influence: Influence "flowed" in but not out. Part three was the in-group's opposite, the companies who were influenced by, but did not own shares in, the SCC companies—this became the out group. Finally, the fourth component of the network consists of the tubes and tendrils, or T&T, companies that remain separate from the SCC but may have ties to members of the in or out groups.

The above illustration actually represents a generic version of a bow tie network, a category of network that can also be used to describe how Web pages are related. The researchers found that the corporate network looked more like the illustration below, which shows that the out group is much larger than the in group or even the SCC.

Only the tiny, elite in group gets to influence the SCC core without submitting to its influence at all. A significant amount of the corporations, however, still fall into the central strongly connected component, which indicates that many of the major market players have complex economic relationships with one another.

"What are the implications for global financial stability?" said the researchers in their paper. "What are the implications for market competition?" The study may not have uncovered a corporate conspiracy, but it does show that corporations are not lone behemoths: They are inter-dependent and influence one another a great deal. Applying a scientific model to the market can help provide a clearer picture of how the world economy runs.

And perhaps a hint at what our corporate overlords are wearing.

Image credit: Stefano Battiston et al., ETH Zurich (Swiss Federal Institute of Technology Zurich)