Natural science is well known for using mathematical models over “common sense” and intuition, to the frustration of many students. The use of mathematics in social sciences is newer, and it is probably fair to say that this discipline is still not as completely reliant on mathematical models as for example modern physics.
However, the ultimate test of the usefulness of mathematical models surely is if it is able to teach us something that our intuition and common sense would not have discovered. And if we can translate these discoveries into practical actions and insights for the modern enterprise allowing large-scale deployment, then we may claim to have advanced human culture in some small way.
An article in The Economist titled Circles of friends (subscription required) summarizes the case for mathematical modeling of human interactions and networks, while the book The Hidden Power of Social Networks, which we discussed earlier, provides the practical application of these insights to the organization of the enterprise.
The article references a study of dolphins who, it turns out, are just as dependent on “mutual friends” to connect groups or cliques as Cross and Parker demonstrated for the large organization. The connectors between tightly integrated groups are a common feature of both human and dolphin relationships, and a key component in determining the overall structure of the organization.
Sometimes you want to strengthen these connectors, as is typically the case in the examples Cross and Parker study, but in other instances you want to weaken these ties. The article mentions terrorist networks but slightly less dramatically we may suggest that there are times when you want elements of the organization to focus on their specific part and for reasons of efficiency not interact unnecessarily with other elements. This can be the case in parts of traditional command and control structures, of which the military is perhaps the classic case.
As for the challenge of providing insights that are not intuitive, the article cites a study of the sexual relationships of high-school students compared with adults. The result is that teenagers are less promiscuous than adults and the chain of connections through sexual partners between two high-school students, when it can be made at all, is much longer on average than the sexual chains between adults in a community. This has important implications for the spread of sexual diseases and how we combat them.
For the enterprise, the lesson is that common sense and intuition is not a substitute for the types of network analysis that Cross and Parker advocates. Often, of course, it is all you have available, but when it is possible to perform an analysis you will usually find elements of the results that surprise you and run against your beliefs.
The science of social network analysis is still in many ways in its infancy, but it can already now deliver real and practical benefits to the enterprise.