diff --git a/Project.toml b/Project.toml
index 54d9fa3..54c1fae 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NamedGraphs"
 uuid = "678767b0-92e7-4007-89e4-4527a8725b19"
 authors = ["Matthew Fishman <mfishman@flatironinstitute.org> and contributors"]
-version = "0.6.0"
+version = "0.6.2"
 
 [deps]
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
@@ -36,7 +36,6 @@ KaHyPar = "0.3.1"
 LinearAlgebra = "1.7"
 Metis = "1.4"
 PackageExtensionCompat = "1"
-Random = "1.7"
 SimpleTraits = "0.9"
 SparseArrays = "1.7"
 SplitApplyCombine = "1.2.2"
diff --git a/README.md b/README.md
index f08b0e1..80f4a88 100644
--- a/README.md
+++ b/README.md
@@ -25,7 +25,7 @@ julia> ] add NamedGraphs
 
 
 
-This packages introduces graph types with named edges, which are built on top of the `Graph`/`SimpleGraph` type in the [Graphs.jl](https://github.com/JuliaGraphs/Graphs.jl) package that only have contiguous integer edges (i.e. linear indexing).
+This packages introduces graph types with named vertices, which are built on top of the `Graph`/`SimpleGraph` type in the [Graphs.jl](https://github.com/JuliaGraphs/Graphs.jl) package that only have contiguous integer vertices (i.e. linear indexing). The vertex names can be strings, tuples of integers, or other unique identifiers (anything that is hashable).
 
 
 
diff --git a/examples/README.jl b/examples/README.jl
index a0a7596..b9e49ae 100644
--- a/examples/README.jl
+++ b/examples/README.jl
@@ -15,7 +15,7 @@
 
 #' ## Introduction
 
-#' This packages introduces graph types with named edges, which are built on top of the `Graph`/`SimpleGraph` type in the [Graphs.jl](https://github.com/JuliaGraphs/Graphs.jl) package that only have contiguous integer edges (i.e. linear indexing).
+#' This packages introduces graph types with named vertices, which are built on top of the `Graph`/`SimpleGraph` type in the [Graphs.jl](https://github.com/JuliaGraphs/Graphs.jl) package that only have contiguous integer vertices (i.e. linear indexing). The vertex names can be strings, tuples of integers, or other unique identifiers (anything that is hashable).
 
 #' There is a supertype `AbstractNamedGraph` that defines an interface and fallback implementations of standard
 #' Graphs.jl operations, and two implementations: `NamedGraph` and `NamedDiGraph`.
diff --git a/src/lib/GraphsExtensions/src/GraphsExtensions.jl b/src/lib/GraphsExtensions/src/GraphsExtensions.jl
index f4a017d..b4d56ea 100644
--- a/src/lib/GraphsExtensions/src/GraphsExtensions.jl
+++ b/src/lib/GraphsExtensions/src/GraphsExtensions.jl
@@ -2,6 +2,7 @@ module GraphsExtensions
 include("abstractgraph.jl")
 include("abstracttrees.jl")
 include("boundary.jl")
+include("neighbors.jl")
 include("shortestpaths.jl")
 include("symrcm.jl")
 include("partitioning.jl")
diff --git a/src/lib/GraphsExtensions/src/neighbors.jl b/src/lib/GraphsExtensions/src/neighbors.jl
new file mode 100644
index 0000000..2e6de9d
--- /dev/null
+++ b/src/lib/GraphsExtensions/src/neighbors.jl
@@ -0,0 +1,8 @@
+using Graphs: AbstractGraph, neighborhood_dists
+
+function vertices_at_distance(g::AbstractGraph, vertex, distance::Int)
+  vertices_and_distances = neighborhood_dists(g, vertex, distance)
+  return map(first, filter(==(distance) ∘ last, vertices_and_distances))
+end
+
+next_nearest_neighbors(g::AbstractGraph, v) = vertices_at_distance(g, v, 2)
diff --git a/src/lib/GraphsExtensions/test/runtests.jl b/src/lib/GraphsExtensions/test/runtests.jl
index b645b64..81f7230 100644
--- a/src/lib/GraphsExtensions/test/runtests.jl
+++ b/src/lib/GraphsExtensions/test/runtests.jl
@@ -69,6 +69,7 @@ using NamedGraphs.GraphsExtensions:
   is_self_loop,
   leaf_vertices,
   minimum_distance_to_leaves,
+  next_nearest_neighbors,
   non_leaf_edges,
   outdegrees,
   permute_vertices,
@@ -81,7 +82,8 @@ using NamedGraphs.GraphsExtensions:
   tree_graph_node,
   undirected_graph,
   undirected_graph_type,
-  vertextype
+  vertextype,
+  vertices_at_distance
 using Test: @test, @test_broken, @test_throws, @testset
 
 # TODO: Still need to test:
@@ -579,5 +581,12 @@ using Test: @test, @test_broken, @test_throws, @testset
   g′ = path_graph(4)
   rem_edges!(g′, [2 => 3, 3 => 4])
   @test g′ == g
+
+  #vertices at distance
+  L = 10
+  g = path_graph(L)
+  @test only(vertices_at_distance(g, 1, L - 1)) == L
+  @test only(next_nearest_neighbors(g, 1)) == 3
+  @test issetequal(vertices_at_distance(g, 5, 3), [2, 8])
 end
 end
diff --git a/src/steiner_tree.jl b/src/steiner_tree.jl
index 1672955..ecffb05 100644
--- a/src/steiner_tree.jl
+++ b/src/steiner_tree.jl
@@ -9,7 +9,11 @@ using SimpleTraits: SimpleTraits, Not, @traitfn
     map(v -> vertex_positions(g)[v], term_vert),
     dist_matrix_to_position_dist_matrix(g, distmx),
   )
-  return typeof(g)(position_tree, map(v -> ordered_vertices(g)[v], vertices(position_tree)))
+  tree = typeof(g)(position_tree, map(v -> ordered_vertices(g)[v], vertices(position_tree)))
+  for v in copy(vertices(tree))
+    iszero(degree(tree, v)) && rem_vertex!(tree, v)
+  end
+  return tree
 end
 
 @traitfn function Graphs.steiner_tree(
diff --git a/test/test_namedgraph.jl b/test/test_namedgraph.jl
index f28f96c..eddaf0f 100644
--- a/test/test_namedgraph.jl
+++ b/test/test_namedgraph.jl
@@ -675,7 +675,8 @@ end
     st = steiner_tree(g, terminal_vertices)
     es = [(1, 2) => (1, 3), (1, 3) => (1, 4), (1, 4) => (2, 4), (2, 4) => (3, 4)]
     @test ne(st) == 4
-    @test nv(st) == 12
+    @test nv(st) == 5
+    @test !any(v -> iszero(degree(st, v)), vertices(st))
     for e in es
       @test has_edge(st, e)
     end