A circular embedding is a graph embedding in a surface that is cellular and has a graph cycle as the boundary of every graph face. The edges in a circular embedding meet only at common endpoints. Because every facial boundary is a graph cycle, the boundary cannot repeat a graph vertex before returning to its starting point. Circular embeddings are also called strong embeddings or closed 2-cell embeddings (Mohar 2010).
The word "circular" refers to these cyclic boundaries, rather than to the placement of the vertices. A circular drawing, by comparison, places the vertices on a circle without requiring the edges to be disjoint. Such a drawing represents a circular embedding only if the edges meet solely at common endpoints and every graph face has a graph cycle as its boundary.
