In a topological graph, what are the edges?

• A. Straight line segments between coordinates
• B. Edges that are always vertical
• C. Continuous curves connecting vertices
• D. Points with no connections

Answer: (C)

Edges are the continuous curves that connect vertices. In a topological graph, what makes an edge meaningful is that you can move along it from one vertex to another without any breaks—the path is continuous. This allows edges to be bent or curved rather than forced to be straight lines, so they aren’t restricted to specific directions or rigid shapes. The endpoints of an edge are the vertices it connects, and the existence of an edge creates the link between those vertices, forming the structure of the graph.

This helps distinguish edges from isolated vertices, which have no connections at all. It also clarifies why describing edges as straight line segments or insisting they be vertical would be unnecessarily limiting in topology—the essential idea is the continuous connection, not a particular geometric form.