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
if the organization seemingly allows Charlie to function without managerial supervision.
Figure 7-14. Alice manages Bob who works with Charlie
However, applying the strong triadic closure principle blindly can lead to some rather odd and uncomfortable-looking organization hierarchies. For instance, if Alice MAN AGES Bob and Charlie but Bob also MANAGES Charlie, we have a recipe for discontent. Nobody would wish it upon Charlie that he’s managed both by his boss and his boss’s boss as in Figure 7-15!
Figure 7-15. Alice manages Bob and Charlie, while Bob also manages Charlie
Similarly, it’s uncomfortable for Bob if he is managed by Alice while working with Charlie who is also Alice’s workmate. This cuts awkwardly across organization layers as we see in Figure 7-16. It also means Bob could never safely let off steam about Alice’s management style!
Figure 7-16. Alice manages Bob who works with Charlie, while also working with Charlie
The awkward hierarchy in Figure 7-16 whereby Charlie is both a peer of the boss and a peer of another worker is unlikely to be socially pleasant, so Charlie and Alice will agitate against it (either wanting to be a boss or a worker). It’s similar for Bob who doesn’t know for sure whether to treat Charlie in the same way he treats his manager Alice (because Charlie and Alice are peers) or as his own direct peer.
It’s clear that the triadic closures in Figure 7-15 and Figure 7-16 are palpably uncom‐ fortable to us, eschewing our innate preference for structural symmetry and rational layering. This preference is given a name in graph theory: structural balance.
Anecdotally, there’s a much more acceptable, structurally balanced triadic closure if Alice MANAGES Bob and Charlie, but where Bob and Charlie are themselves workmates connected by a WORKS_WITH relationship, as we can see in Figure 7-17.
Figure 7-17. Workmates Bob and Charlie are managed by Alice
The same structural balance manifests itself in an equally acceptable triadic closure where Alice, Bob, and Charlie are all workmates. In this arrangement the workers are
in it together, which can be a socially amicable arrangement that engenders camaraderie as in Figure 7-18.
Figure 7-18. Alice, Bob, and Charlie are all workmates
In Figure 7-17 and Figure 7-18 the triadic closures are idiomatic and constructed with either three WORKS_WITH relationships or two MANAGES and a single WORKS_WITH rela‐ tionship. They are all balanced triadic closures. To understand what it means to have balanced and unbalanced triadic closures, we’ll add more semantic richness to the model by declaring that the WORKS_WITH relationship is socially positive (because coworkers spend a lot of time interacting), whereas MANAGES is a negative relationship because managers spend overall less of their time interacting with individuals in their charge. Given this new dimension of positive and negative sentiment, we can now ask the ques‐ tion “What is so special about these balanced structures?” It’s clear that strong triadic closure is still at work, but that’s not the only driver. In this case the notion of structural balance also has an effect. A structurally balanced triadic closure consists of relation‐ ships of all strong sentiments (our WORKS_WITH or PEER_OF relationships) or two rela‐ tionships have negative sentiments (MANAGES in our case) with a single positive rela‐ tionship.
We see this often in the real world. If we have two good friends, then social pressure tends toward those good friends themselves becoming good friends. It’s unusual that those two friends themselves are enemies because that puts a strain on our friendships. One friend cannot express his dislike of the other to us, because the other person is our friend too! Given those pressures, it’s reasonably likely that ultimately the group will resolve its differences and good friends will emerge.
This would change our unbalanced triadic closure (two relationships with positive sen‐ timents and one negative) to a balanced closure because all relationships would be of a positive sentiment much like our collaborative scheme where Alice, Bob, and Charlie all work together in Figure 7-18.
However, another plausible (though arguably less pleasant) outcome would be where we take sides in the dispute between our “friends” creating two relationships with neg‐ ative sentiments—effectively ganging up on an individual. Now we can engage in gossip about our mutual dislike of a former friend and the closure again becomes balanced. Equally we see this reflected in the organizational scenario where Alice, by managing Bob and Charlie, becomes, in effect, their workplace enemy as in Figure 7-17.