A graph in which each edge is associated with a real number, variously termed the "cost," "distance," or "weight."

(n.) a graph with a real number assigned to each edge.

A weighted graph is a graph in which a number (often representing a distance) is assigned to each edge.

a graph in which each edge e is assigned a non-negative number w(e), called the weight of e

a graph whose edges have been assigned numbers - their weights

a graph with a (non-negative) weight for every edge e