Claude Lévi-Strauss was a proponent of Structuralism-flavored anthropology. Kinship is an important example in his *Structural Anthopology*.
This page is an Example.
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Chapter 4 of *Structural Anthropology* is titled “Structural Analysis in Linguistics and in Anthropology.” It’s a good example of the structuralist style of explanation.
In it, Leví-Strauss proposed rules underlying kinship systems in societies where marriage is organized around one man giving a sister or daughter to another. He did this by looking at examples and trying to spot some sort of regularity. And spot it he did.
His claim was that the fundamental building block of such kinship systems consisted of five people, plus two rules.
The five people were a husband and wife, their son and daughter, and the wife’s brother (the son’s maternal uncle).

The family members. Ignore the lines.
Acknowledging that it’s an oversimplification, he classified the relationships between people as what I’ll call either “warm” or “cold.” For example, in some cultures, brothers and sisters aren’t allowed to be under the same roof at the same time. That’s cold. In others, brothers and sisters are so close they sleep in the same bed. Warm.
There are four relationships that matter: between husband and wife, father and son, brother and sister, and finally son and maternal uncle. Given the warm/cold dichotomy, that makes 16 possible combinations of warmth or coldness between the relevant people. But (Lévi-Strauss claims) such human cultures use only four, because of two rules:
1. The relationship of son to father must be the opposite of that between son and maternal uncle. If the society is one where the father gives orders to the son and expects unquestioning obedience, it will be the maternal uncle who’ll spoil the son with gifts and sooth his hurt feelings. Or if the father is indulgent, the uncle must be a stern law-giver.
2. The relationship between husband and wife must be the opposite of that between brother and sister. If husband and wife have a warm, friendly relationship, the son and daughter won’t. If the son and daughter sleep in the same bed, the culture might be one where the wife and husband only meet when the husband sneaks into her separate dwelling place for sex.
It’s convenient to represent all this as a node-and-arrow diagram, so Lévi-Strauss does. Page 45 shows five diagrams, all of the same form. This is my recreation of one such diagram:

Relationships among family members
All five kinship systems have that same form. The only visible difference is whether the line is annotated with a `plus` sign or a `minus` sign to show if the relationship is warm or cold.
You don’t have to draw diagrams to be a structuralist, but structuralism sure lends itself to that.
Lévi-Strauss claims that this combination of people, relationships, and rules is the building block from which all kinship relationships in such societies are built. That is, people build on it to control relationships between cousins, paternal aunts, and so on. However he doesn’t give details in what I’ve read of him, and I don’t know if anyone else followed through combining what Lévi-Strauss called this “atom” of kinship into larger molecules.
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