Is a Loop in a Graph Essentially a Single-Step Cycle?

Absolutely, a loop (or self-loop) qualifies as a cycle of just one step.

This perspective stems from the definition of a cycle in graph theory, which is a closed path that starts and ends at the same vertex without revisiting any vertices in between.

A loop, connecting a vertex back to itself, aligns perfectly with this definition. The distinctive aspect here is that the journey begins and ends at the same vertex without the need to traverse any other intermediate vertices.

Hence, viewing a loop as a one-step cycle is a precise and insightful way to understand its role within graph theory.

It also serves as an exemplary concept for delineating the differences between loops and cycles, highlighting how even the most elementary structures can illuminate the broader complexities of networks and their characteristics.