Census of Triads

January 27, 2017

Moreno’s sociogram and subsequent census of triads provides what some call the DNA of social networks. Figure 1 illustrates sixteen possible configurations of these triads. Each vertex represents an actor/agent, and each edge represents a connection through which information, currency, or some other measurable phenomenon flows. The directed edges indicate the direction of flow and its reciprocity between agents.


Figure 1: Census of Sixteen Network Triad Configurations




The distribution of triads (and dyads) in a network can be compared to randomly generated graphs with the same number of vertices and varying probability that they will share edges, i.e. network density (Lu 2011). Figure 2 illustrates the census history of an iterated random network with 12 vertices and a 0.2 probability of sharing edges.


Figure 2: Network Triad Type in Randomly Generated Networks P = 0.2



The network in Figure 2 was iterated only ten times, however a clear distribution emerges. Triads with shared reciprocity are less probable. However, as network density increases with a probability of 0.6, we see a different trend emerge in Figure 3.


Figure 3: Network Triad Type in Randomly Generated Networks P = 0.6




If measuring, for example, the flow of information through a network, we would expect a dense network to generate reciprocity at a higher rate. Of note, binding mechanisms (Borgatti et al. 2009), where a node distributes information or resources to two unconnected notes, suggest that position could gain a competitive advantage by playing the unconnected nodes against one another.


What will be interesting is conducting experiments to see how different triads work in small world networks in the dissemination of information that then influences human behavior and preferences, such as voting.


Illustrations generated in Mathematica 11






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