August 24, 2026
After talking with a friend (Vivian, see her website here), we realized that social networks could be discussed in mathematical languages. Luckily, our languages are different and I think she will describe her version in a later post. For myself, I visualized it more like a graph with simple rules with people acting as nodes with edges representing links. This is not a novel operation; social networks are described as much for a reason! However, we quickly came across a few dynamics which create interesting network shapes and explain some facets of the question of modern day lonliness. I also made a simulator for this post here.
A location represents a bag of nodes in which nodes (N) are more likely to form links due to geographic proximity. Given the internet and mobility, links may be made between locations, but these are much less likely. Within each location, nodes have a base rate of creating a link, this rate being a function of the physical factors of the location, human sociability, etc. When people discuss the lonliness criss, what they are typically pointing out is a decrease in this base rate leading to less overall links. However, there are nodes (N+) which display a much higher ability to form links with all other nodes. This is due to being generally likable, immersing themselves in more social contexts, etc. These result in hyperconnected networks which are more likely to form (N+/N+) links, though they individually have many (N+/N) links. N/N links exist as well, at a far lower rate. It was then we realized that this explains two facts.
First, this is an independent discovery of the finding that most’s friends are more likely to have more friends than them. If this + category were more realistic, it would be a gradient of sociality such that a higher + score results in more connections, and as this scales, higher + scores are more likely to link with outher high-plus scores, resulting in a more connections per person while iterating over an ordered list of one’s friends.
Second, this creates Aella’s slutcloud. Just the + category reinforces a large number of links between nodes, a higher level of sexual availability would do the same. Given that there is a degree of sociability distinct from the average creating a dense interconnected center of nodes with more sparsely connected ones at the outside, the same must be true for any trait which operates at a higher propsensity for connectiveness.
Groups (G) form within locations due to a shared social context such as office hours, university, hobbies, and interests. These increase the likelihood of connection above the baseline due to a further increased chance of interaction. We may define these as sets A, B, … such that each belongs to at least one set, but some belong to multiple groups. Thus, clouds form in these groups but will form occasional connections to others. These effects can be strong; one rarely makes non-college friends while they are in it! The odds of any person off the street forming a link with another is quite low.
There are some nodes which refuse to be connected to other nodes, or connected with nodes which are within a certain number of links of other nodes. We can represent these as shapes, where normal nodes are circles, hypersocial nodes are stars, and nodes which refuse to be within n links of those with a different shape may be squares and triangles. This may be due to a particular dislike of some trait one person has or other social friction. “Cancellation” may be another, and so on. This repulsion will make an oddly-shaped graph such that some are isolated on the edges despite odds of generating a link. As expected, those with more restrictive criteria are more likely to be on the edges of the cloud. However, these restrictive nodes may also trap multiple other nodes on the outskirts of the graph despite the “innocent” propensities for connection. Because of this, we have groups which are strangely divided from other groups or those who remain unconnected.
The natural assumption, with the probability of linkage being greater than zero with an infinite time would be that every node forms a connection with every other node regardless of group. Eventually, the N/N+ distinction and G memberships would cease to matter. There are real-world contraints on this (Dunbar’s number, lifespan) which prevent this from occuring. Further, with the addition of link constraints, more realistic, with sub-network isolation occuring, even within groups! These rules introduce strange network contortions which explain the formation of clouds based around N+ nodes. A N+ node will inevitably vform a connection with a negative-trait node which constrain its future linkages. If the goal of sociality were to create the maximum number of linkages, the optimal move would be to sever the link with the problematic node. Luckily friendships are not thrown away so easily, creating these less-than-optimal graphs. Though perhaps all the squares ought to belong in their own corner opposite the triangles such that others are not forced to choose.
Just as sociality should be a continuous variable, so should the rest of these traits to create a more realistic-looking graph. As well, there are groups with different intergroup link probability than other groups (think board game fans versus those who enjoy clubbing). Individual nodes may also have different limits on the number of links that they can maintain as well as their toleration for specific traits. Generally, these may be ignored to create the above default network rules.
One should probably aim to have a higher propensity for links than the base rate nodes. This does not solve the inherent issue with base rates, but it is still better than being a default node. Any trait which causes one to be a constrained node will likely pose an issue as well (though sometimes, one cannot help themselves). While being a node with a high number of links is good, attempting to target this alone neglects the actual point of socialization and I do not want to encourage Goodharting. Rather, this is one possible framework to play with.