I am reading the following paper on Rectangular Cartograms - http://ac.els-cdn.com/S0925772106000770/1-s2.0-S0925772106000770-main.pdf?_tid=ce3aa43e-cef1-11e3-b342-00000aacb361&acdnat=1398702556_1adee439a6b55c82efa20917178fb0aa and I am totally confused as to what this statement says on Page-177 in the Algorithmic Outline section of the paper
"Assume that we have an administrative subdivision into a set of regions. The regions and adjacencies can be represented by nodes and arcs of a graph F, which is the face graph of the subdivision."
Now there are a couple of questions I would like to ask :
1) What is meant by administrative subdivision into a set of regions?
2) What is meant by a Face Graph?
1) An administrative subdivision into a set of regions likely means a division of a region into several subregions. For example, the United States is divided into 50 states.
2) The face graph is a graph with a vertex corresponding to each region, where two vertices are connected by an edge if and only if the corresponding regions share a border.