Have you ever tried to explain relationships from a romance book, film or a soap opera to a friend? Not so easy task if there are too many people and connections between them. Next time you can try to draw it on a piece of a paper or on a napkin in a restaurant.
Note: I will try to moderate myself and try to not to use too mathematical language when describing social networks, even the descriptions would be more precise.
We begin with some basics: persons and places. Well, instead of person more general would be to use term entity, as it can be a horse, dog, company or anything you can think of.
Situation focus is an entity (or a person) of main interest to the situation, main hero. Or ot can mean
self or the story narrator, the person who describes the situation. Or... it can be a person to which a situation is described to as well, just make it clear what is the focus.
Group represents, surprisingly a group of people, group of entities or a community.
Place can be part of the social network graph if it is relevant to the described situation. It can be room, building, city, state, or even non specified place (meaning "somewhere").

The entities are connected, and together with links they form a network or better a graph.
People are strangers to each other when they do not know each other. This fact is depicted by not putting a link between the people. However, note that the diagram can be created by third person, not involved in the described situation. Or the creator does not have full knowledge of the situation. Or just simply the relationship is not relevant to the situation being described. Because of that, missing connection does not necessarily has to mean that the there is no link between the people.
Friends will be friends... Remember that one? Queen. Anyway, I am using the term friends for simplicity, as majority of such links would represent that the persons are mutual friends. However, it can be considered as any simple link where entities interact quite frequently and they most likely have contacts to each other. To the contrary, acquaintances just know about each other's existence, they interact very rarely or rather randomly, and do not have to have contact to each other. Partners are more than friends. There is stronger binding between the two. In some cases the link can represent a binding by contract or marriage. Some people just know about other people, but the reverse knowledge does not exist or we just do not know about it. And of course, unbalanced relationships exist as well.
Knowing the social networks graphical language basics we can try to explain a situation at a party where eleven old friends met:

Coming up next: Meta connections, or connections to connections.