Preserving labels when using graph functions

Question

I am finding that some functions that accept a graph and return a transformed graph lose all the vertex and edge labels of the graph being transformed. For example, when I define a graph like this:

g = Graph[{
      Property["a" -> "b", EdgeLabels -> "one"], 
      Property["b" -> "c", EdgeLabels -> "two"],
      Property["c" -> "d", EdgeLabels -> "three"],
      Property["a" -> "c", EdgeLabels -> "four"]},
      VertexSize -> Medium, VertexLabels -> Placed["Name", Center]]

The graph g has both edge and vertex labels. Now, I would like to create a neighborhood graph around vertex "a":

NeighborhoodGraph[g, "a"]

When I do this, I find that the new graph created does not have vertex or edge labels. I would like to be able to use these graph manipulation functions, but I need to keep the graph attributes. A graph with no labels is not very useful to me. Any help is appreciated!

Answer 1

 NeighborhoodGraph[g, "a", Options[g]]

gives

Answer 2

Method 1: PropertyValue

This is the standard way for manipulating graph properties:

NeighborhoodGraph[g, "a", 
 EdgeLabels -> PropertyValue[g, EdgeLabels], 
 VertexLabels -> PropertyValue[g, VertexLabels], 
 VertexSize -> PropertyValue[g, VertexSize]]

which can be simplified to:

NeighborhoodGraph[g, "a", 
(# -> PropertyValue[g, #]) & /@ {VertexLabels, EdgeLabels, VertexSize}]

---

Method 2: HighlightGraph (following Sjoerd's suggestion)

This takes Sjoerd's approach but hides the part of the graph that you do not want to see. I generally prefer it to the above method because it preserves the location of the vertices and the shape of the edges.

HighlightGraph[g, NeighborhoodGraph[g, "a"], GraphHighlightStyle -> "DehighlightHide"]

---

Method 3: AbsoluteOptions (Not recommended)

This works (usually):

NeighborhoodGraph[g, "a", AbsoluteOptions[g, {EdgeLabels,VertexLabels,VertexSize}]]

AbsoluteOptions behaves inconsistently and thus should probably be avoided.

Answer 3

Though this is probably not what you're looking for, HighLightGraph can be useful to mark subgraphs in the original graph. In your case:

HighlightGraph[g, NeighborhoodGraph[g, "a"]]