What is a loop in a graph?

A loop is an edge that connects a vertex to itself.

Formally: If an edge connects a vertex v to itself, it is a loop: (v, v).

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#Example

If a graph has a vertex A, and an edge goes from A → A, that is a loop, the vertex "refers" to itself.

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#Features

• A loop can occur in both directed and undirected graphs.
• It increases the degree of the vertex: in an undirected graph, a loop adds 2 to the degree, in a directed graph, 1 to the in-degree and 1 to the out-degree.

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#Interpretation

• In a social network, a user interacts with themselves.
• In automata, a state from which the system can remain in the same state.

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Summary: a loop is an edge that starts and ends at the same vertex.