What is the contour of a graph I am reading the paper "A Linear-time Algorithm for Drawing
a Planar Graph on a Grid" and it says:
let w1  , ..., wm be the contour of Gk-1
where Gk-1 seems to be either a graph, or the embedding of a graph. What does the "contour" of graph mean? I am trying to search for "contour graph" and I am only getting the geographic meaning.

The geographical idea can be extended for graphs.
Most generally, a contour is a set of points that share a common measure.
The most obvious definition in your case would be the set of points that are a certain number of steps away from a perhaps arbitrarily chosen central point.
At the start of the algorithm, the contour (distance 0) would be the first chosen point.
At the end of the first iteration, the contour would be the set of vertices that are distance 1 from the first chosen point. I'm guessing that $G_{k-1}$ would be the subgraph created from the vertices that are distance 1 or less away from the first chosen point.
