The problem appears first in Kochen and Pool's paper, which circulated from roughly 1960 to 1978, when it was published as the inaugural paper of the journal Social Networks. Kochen and Pool where able to adequately phrase the question, but admittedly, even after 20 years, found no solution to it: the question goes: given a set N of people, what is the probability that each member of N is connected to another member via k_1, k_2, k_3...k_n links?

The theoretical question has seen an explosion of research over the last 30 years, especially in the field of graph theory and social network analysis.

It was Stanley Milgram, the social Psychologist, who first formulated it as an empirical research question in a 1967 experiment funded by the Harvard Council on Social Relations. Here he asked the same question, but his answer was a statistical one which took elegant advantage of individuals and the postal system.

Milgram and the science of social networks focuses on the network itself, especially the complex ones. It is not interested in what anthropologists have traditionally focussed on, namely the kinship relations of the people involved. What's the difference?

To begin with, there is a classic distinction in anthropology. Emic vs. Etic. The explanation that we as observers give of any phenomena can be different from the explanation that those observed themselves might give. In terms of kinship, this has often resulted in a distinction between, e.g. biology as the 'objective' criteria of relations and family ties, kin relations, or other supposedly 'subjective' terms. However, it is also possible to study the way people relate to each other on the basis of what they know (or think they know) about biology and genetics.

The small world problem doesn't capture this difference. In fact it doesn't care about it at all. All that matters is that there is a connection-- it could be biological, genetic, by marriage, friendship, through work or school or any other kind of reason for humans to know and iteract with each other. The question it does ask is "what does the overall system of relationality in the world look like?" Who is connected to who and how? It is concerned with an abstract "shape" of society and is therefore quite amenable to the mathematics of graph theory and topology.

However, the anthropological question does not go away. Just as people can describe their relationships with each other on the basis of their understanding of biology, so to might they describe their relations on the basis of their understanding of a network. The phrases "six degrees of separation" and "its a small world after all" are just two examples of such explanations. Some people who understand how the internet and the telecommunications system work might have a different understanding of the shape of society from those people who only ever talk with their neighbors and the mail man. What difference does it make to have a different understanding of the shape of society?