Representations of Social Networks

In my study of social networks, I keep asking myself why they are commonly represented so simply? The concept of a "graph" is simple enough, and many of the natural extensions I'd like to see never seem to come up.

An artificial graph, below, contains 3 nodes (people), 2 edges (friendships), and 1 "non friendship).



Let's assume you're trying to assess triadic closure (the propensity for B-C to become friends if A-B and A-C are friends). What would be helpful for this graph would be:
1. The nature of the edge between A-B and A-C.
- Are the edges representing true friendships?
- Are the edges actually a blend of two types of edges (professional/ affiliate and personal)? "A" may be great personal friends with "B", but belong to the same club as "C". This is unlikely to drive triadic closure.
2. The weight of the edge between A-B and A-C. Something that has always made me uncomfortable is the qualitative nature of how edges are described. Perhaps because this is, historically, difficult to quantify. Even so, a 1= acquaintence, 2=best friend would add a more comfortable quantitative layer.
3. The nature of the edges between pairs are unidirectional, when stated/ perceived relationships by the individuals within the pairs may not be reciprocal. I'd like to see every edge actually be made up of 2 edges: one for the nature perceived by each node.

Lastly, flying in the face of the triadic closure concept, I'd like to see ties with a weight ranging from -1 (avoidance) to +1 (closeness); 0 would represent non-friendship/ non-tie. If A-B are friends and B-C are friends, and A is a drug dealer, and C is a recovering addict, triadic closure likely won't result here.

I'd think adding these details would provide a more nuanced analysis. Perhaps as I dig a bit deeper, these practices will surface.