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I want to add a new vertex to a graph, with fixed VertexCoordinates but when I use VertexAdd, the new graph does not have the VertexCoordinates of the previous one.

g = Graph[{1 -> 2}, VertexCoordinates -> {{0, 0.5}, {0.5, 0}}, 
  PlotRange -> 1]

This is the initial graph

g = VertexAdd[g, 3]

Adding a new vertex makes a new graph with automatic coordinates.

I tried to see if there is a way to define the coordinates when adding a new vertex but I could not find anything.

Also I was looking if there is something like:

SetProperty[g, VectorCoordinates -> {list of coordinates}]

To set coordinates for all vertices in a graph, but I could not find anything.

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Here is your Graph

g = Graph[{1 -> 2}, VertexCoordinates -> {{0, 0.5}, {0.5, 0}},PlotRange -> 1]

You can try this!

g = SetProperty[VertexAdd[g, {3, 4}],
VertexCoordinates-> PropertyValue[g, VertexCoordinates]~Join~{{.7, .6}, {-.2, -.3}}];

The graph will retain its VetexCoordinates

EdgeAdd[g, 1 -> 4]

enter image description here

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