How to Delete Edges Given Specific Vertex Labels?

Question

Given the following directed graph, is there a way to delete all edges that contain a specified vertex label name. For instance, suppose the edge list below was read in. Any edge in that list with a vertex labeled by x would be deleted, along with the vertices on both sides of that edge. For example, in the edge list below, the graph would be generated for just the edges N4 -> N5, N6 -> N2, N6 -> N3, N6 -> N4, N1 -> N8, N2 -> N8, N4 -> N8, N7 -> N8, N9 -> N7, N9 -> N8

edges = {N1 -> x, x -> N3, x -> x, N4 -> N5, N6 -> N2, N6 -> N3, 
  N6 -> N4, N1 -> N8, N2 -> N8, N4 -> N8, N7 -> N8, N9 -> N7, N9 -> N8}
g = Graph[edges, VertexLabels -> Automatic]

Answer 1

You can use VertexDelete[g,v] to delete vertex $v$ and all edges connected to $v$.

VertexDelete[g, x]