# Graph where every node have some value

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?