What is the definition of an weighted graph?

$\begingroup$

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 .

$\endgroup$ 1

4 Answers

$\begingroup$

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.

$\endgroup$ $\begingroup$

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)

$\endgroup$ $\begingroup$

Weighted graph is a graph in which real number is associated with each edge of graph..

$\endgroup$ $\begingroup$

A weighted graph is also directed graph with weight on the edge of each graph

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy