What is the definition of an weighted graph?

Question

In graph theory which one of these two will be called a weighted graph ?

1. A graph where vertices have some weights or vales .
2. A graph where edges have some weights or values .
3. A graph where both edges and vertices have some weights or values
4. A graph where neither edges nor vertices have any weights or values

I couldn't find a picture for the third case actually .

Answer 1

There is some variation in the literature, but typically a weighted graph refers to an edge-weighted graph, that is a graph where edges have weights or values. Without the qualification of weighted, the graph is typically assumed to be unweighted.

Answer 2

Answer choice (2) according to one popular text:

With each edge $e$ of $G$ let there be associated a real number $w(e)$, called its weight. Then $G$, together with these weights on its edges, is called a weighted graph.$^1$

[1] Bondy and Murty. Graph Theory with Applications. North-Holland, 1976 (page 15-16)