Earlier this semester, we discussed labeling the edges of a graph. A plus was given if the two nodes were friends, and a minus was given if the two nodes were enemies. This paradigm worked well in describing relationships among people. Not surprisingly, pluses and minuses can also be used to characterize relationships among firms. But one question does arise: how should you assign pluses and minuses to each edge? In “Competition, Mutualism, and Organizational Outcomes: The Effects of Domain Overlap and Non-Overlap on Organizational Performance, Growth, and Survival,” Heather Haveman and Lisa Keister describe a two dimensional relationship structure. This structure can be used in a firm network graph to determine the positive and negative edges. The first dimension describes how similar the firms are, and varies from commensalism (having a lot in common) to symbiosis (being dissimilar). The second dimension deals with relations between companies, and goes from competition to mutualism.[i]

            To see how Haveman and Keister’s classification can be used to determine the pluses and minuses, let’s consider a one industry example with a set of downstream firms and a set of upstream firms. Here, there might only be two types of relations: (1) relationships between firms that have a lot in common and are competing with each other, and (2) relationships between firms which are dissimilar but have mutual interests. The first category would describe companies at the same level of production, while the second would describe businesses at different stages.[ii] Pairs of nodes that fall into number one would get a minus, and pairs that fall into number two would get a plus.

            One thing missing from the diagram is the magnitude of competition and mutualism (i.e. the magnitude of the plus and minus). To address this, a term from Haveman and Keister’s overlap density measure can be placed along each edge[iii]. Let v and u be M x 1 vectors describing the types of sweaters firms v and u make. For example, if v makes a sweater in category 3, a 1 is placed in the third row. Dotting v and u and dividing by the magnitude of v will give you a measure of v’s competiton with u. The same can be done in the other direction with u. Mutualism could also be done in this way, except a 1 would be placed in a supplier’s row if it made supplies for that type of sweater.  

Unfortunately, I could not find an online version of the book chapter; however, I do have links to the authors’ websites:

http://www0.gsb.columbia.edu/whoswho/full.cfm?id=55582

http://www.soc.duke.edu/~lkeister/

[i] Haveman, Heather A., and Lisa A. Keister. “Competition, Mutualism, and Organizational Outcomes: The Effects of Domain Overlap and Non-overlap on Economic Performance, Growth, and Survival.” In The Sociology of the Economy, edited by Frank R. Dobbin.
New York: Russell Sage, 2004. Page 231.

[ii] Haveman and Keister. Page 232.

[iii] Haveman and Keister. Page 241.