# Definition:Weight Function

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## Definition

A **weight function** on a set $S$ is a mapping from $S$ to the real numbers:

- $w: S \to \R$

It is common for the requirements of a specific application under discussion for the codomain of $w$ to be restricted to the positive reals:

- $w: S \to \R_{\ge 0}$

The thing that determines whether a given mapping is a **weight function** depends more on how it is used.

## Also see

- Definition:Weighted Graph, the application of a
**weight function**to the edges of a graph.