Predictive Analysis with Graph Theory - Graph Databases - page 176

Figure 7-13. Bob and Charlie work together under Alice
Because Bob and Charlie both work with Alice, there's a strong possibility they're going
to end up working together, as we see in Figure 7-13 . This is consistent with the strong
triadic closure property, which suggests that either Bob is a peer of Charlie (we'll call
this a weak relationship) or that Bob works with Charlie (which we'll term a strong
relationship). Adding a third WORKS_WITH or PEER_OF relationship between Bob and
Charlie closes the triangle—hence the term triadic closure .
The empirical evidence from many domains, including sociology, public health, psy‐
chology, anthropology, and even technology (e.g., Facebook, Twitter, LinkedIn), sug‐
gests that the tendency toward triadic closure is real and substantial. This is consistent
with anecdotal evidence and sentiment. But simple geometry isn't all that's at work here:
the quality of the relationships involved in a graph also have a significant bearing on
the formation of stable triadic closures.
Structural Balance
If we recall Figure 7-12 it's intuitive to see how Bob and Charlie can become coworkers
(or peers) under Alice's management. For example purposes, we're going to make an
assumption that the MANAGES relationship is somewhat negative (after all, people don't
like getting bossed around) whereas the PEER_OF and WORKS_WITH relationship are pos‐
itive (because people like their peers and the folks they work with).
We know from our previous discussion on the strong triadic closure principle that in
Figure 7-12 where Alice MANAGES Bob and Charlie, a triadic closure should be formed.
That is, in the absence of any other constraints, we would expect at least a PEER_OF , a
WORKS_WITH , or even a MANAGES relationship between Bob and Charlie.
A similar tendency toward creating a triadic closure exists if Alice MANAGES Bob who in
turn WORKS_WITH Charlie, as we can see in Figure 7-14 . Anecdotally this rings true: if
Bob and Charlie work together it makes sense for them to share a manager, especially