Simmel's classic article on The triad can be seen as the seminal article on networks and brokerage and, probably most correctly, as largely before its time in its treatment.
Simmel uses the article as a means of offering an ontology of different types of three-person relationships or, describing the sociological significant of the third actor.
The first type is the non-partisan or the mediator. The example Simmel gives is a child in a marriage who has the function of holding the marriage together. This can happen either by strengthening a relationship between two or by creating a new indirect relationship between two people. Non-partisan can either stand equally between two positions or can stand "above" them in some sense.
The tertius gaudens is perhaps the most influential piece of the short article and describes the "third who benefits." The idea of the tertius gaudens is that it is a person who keeps people apart and who, as the gateway between the two, can extract rents. Either, the tertius can encourage the other two to compete for their favor. As the broker, the tertius can play the two sides off each other. Simmel describes the extreme form of the tertius as the buying public on a market and argues that the advantage accruing to the tertius derives from the face that, "he has an equal, and equally independent, and for this very reason, decisive, relation to the two others."
The final major type is divide et impera (divide and rule) which is someone who creates conflict in order to gain a dominating position. This might be done through distribution of assets in such a way that creates jealousy and fighting. The most active form would actually attempt to unleash a fight between two groups.
Theoretical and Practical Relevance
Simmel's short piece can be seen as the basis of much of the social network literature and, in particular, the literature on brokerage and structural holes.
An in-depth summary can be found at: