Graph where every node have some value

Question

Is there any type of weighted directed graph which is also having another property which is stored value for every vertex.

so then the graph definition will look something like:

$E = \{a,b,c,d\}$

$V = \{(a,b),(b,c),(c,d),(d,a)\}$

$W = \{(a,b)\mapsto 0.1,(b,c)\mapsto 0.2,(c,d)\mapsto 0.3,(d,a)\mapsto 0.4\}$

$ X = \{a\mapsto 25,b\mapsto 35,c\mapsto 15,d\mapsto 25\} $

It is exists , how it is called?

Answer 1

I found an interesting paper you might be interested in: doubly weighted graph in the paper such graphs are called doubly weighted graphs but there might be other names as this seems to be merely a descriptive one.