From a mathematical perspective many problems in anthropology concerned with the analysis of structures, patterns, and configurations are combinatorial in nature. There are three types of combinatorial problems:

1. The existence problem asks, “Is there a structure of a certain type?”

2. The counting problem asks, “How many such structures are there?”

3. The optimization problem asks, “Which is the best structure according to some criterion?” (Roberts 1984).

The minimum spanning tree problem (MSTP) is an optimization problem, well known in many fields; its history is detailed in Graham and Hell (1985). The problem has applications to the design of all kinds of networks, including communication, computer, transportation, and other flow networks. It also has applications to problems of network reliability and classification, among many others. Our purpose here is to describe some applications of the MSTP to anthropology – in particular to problems of size, clustering, and simulation in networks of various kinds. We proceed by presenting in a unified format the three standard MST algorithms of Kruskal (1956), Prim (1957), and Boruvka (1926a,b), describing the advantages and some of the applications of each one.

We first illustrate the MSTP intuitively, as follows. A large corporation with offices in many cities, v1, …, vn, wishes to determine the monthly telephone charge. All the distances d(vi, vj) are known and are distinct.