Q:

How to label the Vertex and, or Edge labels with their weight

I noticed that the Mathematica 9.0 documentation only mentions the usage of "Name" to label the vertexlabel or edgelabel in the Graph.
Is there an option to use the Weights automatically just as "Name" does?

A:

I found that "EdgeWeight" and "VertexWeight" are next to "Name" also possible candidates. 
Graph[{1 \[UndirectedEdge] 2, 2 \[UndirectedEdge] 3, 
  3 \[UndirectedEdge] 1}, VertexWeight -> {100, f[x], 300}, 
 EdgeWeight -> {10 || 20, Prime[x], g[x]^2}, 
 VertexLabels -> "VertexWeight", EdgeLabels -> "EdgeWeight", 
 ImagePadding -> 20]

