The exponential growth of possible connections as networks expand (see previous post) makes them hugely valuable, but comes with its own set of costs.
Keeping track of relational dynamics gets complicated fast. In a pair, you’ve got one relationship to keep an eye on. In a triplet, you’ve got two lines of communication that you’re directly involved in and an additional line (between the other two group members) that you need to track.
And it’s dynamic: these relationships interact and affect each other, so that a change in quality or tone of one relationship will cause change and adaptation in the others. The diagram above really needs an extra layer of lines between the lines.
This is before counting the subgroups that emerge in larger networks, each of which has its own dynamics and interactions. Adding a fourth person takes the number of paired connections to six, but also creates four possible triplets, each exerting its own influence on the other triplets and paired connections.
Here’s a table showing how the number of subgroups grows up to a network size of ten, made using this rather nice formula in excel:
| Possible subgroups of each size | ||||||||||
| Network size | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Total Possible Groups |
| 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 (0.5*n) |
| 3 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 (2*n) |
| 4 | 6 | 4 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 11 |
| 5 | 10 | 10 | 5 | 1 | 0 | 0 | 0 | 0 | 0 | 26 |
| 6 | 15 | 20 | 15 | 6 | 1 | 0 | 0 | 0 | 0 | 57 (10*n) |
| 7 | 21 | 35 | 35 | 21 | 7 | 1 | 0 | 0 | 0 | 120 |
| 8 | 28 | 56 | 70 | 56 | 28 | 8 | 1 | 0 | 0 | 247 |
| 9 | 36 | 84 | 126 | 126 | 84 | 36 | 9 | 1 | 0 | 502 |
| 10 | 45 | 120 | 210 | 252 | 210 | 120 | 45 | 10 | 1 | 1013 (100*n) |
Politics and Disinformation
As a final layer of complexity, consider that groups of people don’t consist of value-neutral nodes communicating accurate information with perfect accuracy. Rather, they’re made up of humans, with all of the different interests, idiosyncrasies, miscommunications, bad information, hidden agendas, and possibilities for manipulation that that implies. Each additional person and group in the network adds exponentially more information to filter and consider.
So what?
This is why planning family reunions is difficult.