libgraph v0.6.3 Graph

This module defines a directed graph data structure, which supports both acyclic and cyclic forms. It also defines the API for creating, manipulating, and querying that structure.

This is intended as a replacement for :digraph, which requires the use of 3 ETS tables at a minimum, but up to 6 at a time during certain operations (such as get_short_path/3). In environments where many graphs are in memory at a time, this can be dangerous, as it is easy to hit the system limit for max ETS tables, which will bring your node down. This graph implementation does not use ETS, so it can be used freely without concern for hitting this limit.

As far as memory usage is concerned, Graph should be fairly compact in memory, but if you want to do a rough comparison between the memory usage for a graph between libgraph and digraph, use :digraph.info/1 and Graph.info/1 on the two graphs, and both contain memory usage information. Keep in mind we don’t have a precise way to measure the memory usage of a term in memory, whereas ETS is able to give a precise answer, but we do have a fairly good way to estimate the usage of a term, and we use that method within libgraph.

The Graph struct is composed of a map of vertex ids to vertices, a map of vertex ids to their out neighbors, a map of vertex ids to their in neighbors (both in and out neighbors are represented as MapSets), a map of vertex ids to vertex labels (which are only stored if a non-nil label was provided), and a map of edge ids (which are a tuple of the source vertex id to destination vertex id) to a map of edge metadata (label/weight).

The reason we use several different maps to represent the graph, particularly the inverse index of in/out neighbors, is that it allows us to perform very efficient queries on the graph without having to store vertices multiple times, it is also more efficient to use maps with small keys, particularly integers or binaries. The use of several maps does mean we use more space in memory, but because the bulk of those maps are just integers, it’s about as compact as we can make it while still remaining performant.

There are benchmarks provided with this library which compare it directly to :digraph for some common operations, and thus far, libgraph is equal to or outperforms :digraph in all of them.

The only bit of data I have not yet evaluated is how much garbage is generated when querying/manipulating the graph between libgraph and digraph, but I suspect the use of ETS means that digraph is able to keep that to a minimum. Until I verify if that’s the case, I would assume that libgraph has higher memory requirements, but better performance, and is able to side-step the ETS limit. If your requirements, like mine, mean that you are dynamically constructing and querying graphs concurrently, I think libgraph is the better choice - however if you either need the APIs of :digraph that I have not yet implemented, or do not have the same use case, I would stick to :digraph for now.

Link to this section Summary

Functions

Gets the shortest path between a and b

Adds an edge connecting a to b. If either a or b do not exist in the graph, they are automatically added. Adding the same edge more than once does not create multiple edges, each edge is only ever stored once

Like add_edge/3, but takes a list of Graph.Edge structs, and adds an edge to the graph for each pair

Adds a new vertex to the graph. If the vertex is already present in the graph, the add is a no-op

Like add_vertex/2, but takes a list of vertices to add to the graph

Returns the root vertex of the arborescence, if one exists, otherwise nil

Returns a list of connected components, where each component is a list of vertices

Removes an edge connecting a to b. If no such vertex exits, or the edge does not exist, it is effectively a no-op

Like delete_edge/3, but takes a list of vertex pairs, and deletes the corresponding edge from the graph, if it exists

Removes a vertex from the graph, as well as any edges which refer to that vertex. If the vertex does not exist in the graph, it is a no-op

Like delete_vertex/2, but takes a list of vertices to delete from the graph

Gets the shortest path between a and b

Returns the label for the given vertex. If no label was assigned, it returns nil

Return a list of all the edges, where each edge is expressed as a tuple of {A, B}, where the elements are the vertices involved, and implying the direction of the edge to be from A to B

Builds a list of paths between vertex a and vertex b

Returns true if the given vertex exists in the graph. Otherwise false

Returns the in-degree of vertex v of graph g

Returns a list of Graph.Edge structs representing the in edges to vertex v

Returns a list of vertices which all have edges coming in to the given vertex v

Returns a map of summary information about this graph

Returns true if and only if the graph g is acyclic

Returns true if the graph is an aborescence, a directed acyclic graph, where the root, a vertex, of the arborescence has a unique path from itself to every other vertex in the graph

Returns true if the graph g is not acyclic

Returns true if graph g1 is a subgraph of g2

Returns true if and only if the graph g is a tree

Updates the label for the given vertex

Returns a list of vertices from graph g which are included in a loop, where a loop is a cycle of length 1

Creates a new graph

Returns the number of edges in the graph

Returns the number of vertices in the graph

Returns the out-degree of vertex v of graph g

Returns a list of Graph.Edge structs representing the out edges from vertex v

Returns a list of vertices which the given vertex v has edges going to

Returns all vertices of graph g. The order is given by a depth-first traversal of the graph, collecting visited vertices in postorder. More precisely, the vertices visited while searching from an arbitrarily chosen vertex are collected in postorder, and all those collected vertices are placed before the subsequently visited vertices

Returns all vertices of graph g. The order is given by a depth-first traversal of the graph, collecting visited vertices in preorder

Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it v), there is a path in the graph from some vertex of vs to v

Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it v), there is a path in the graph of length one or more from some vertex of vs to v

Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it v), there is a path from v to some vertex of vs

Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it v), there is a path of length one or more from v to some vertex of vs

Replaces vertex with new_vertex in the graph

Splits the edge between v1 and v2 by inserting a new vertex, v3, deleting the edge between v1 and v2, and inserting an edge from v1 to v3 and from v3 to v2

Returns a list of strongly connected components, where each component is a list of vertices

Builds a maximal subgraph of g which includes all of the vertices in vs and the edges which connect them

Converts the given Graph to DOT format, which can then be converted to a number of other formats via Graphviz, e.g. dot -Tpng out.dot > out.png

Returns a topological ordering of the vertices of graph g, if such an ordering exists, otherwise it returns false. For each vertex in the returned list, no out-neighbors occur earlier in the list

The transposition of a graph is another graph with the direction of all the edges reversed

Updates the metadata (weight/label) for an edge using the provided options

Returns the label for the given vertex. If no label was assigned, it returns nil

Returns a list of all the vertices in the graph

Link to this section Types

Link to this type t()
t() :: %Graph{edges_meta: %{optional({vertex_id, vertex_id}) => map}, in_edges: %{optional(vertex_id) => MapSet.t}, out_edges: %{optional(vertex_id) => MapSet.t}, vertex_labels: %{optional(vertex_id) => term}, vertices: %{optional(vertex_id) => vertex}}
Link to this type vertex()
vertex() :: term
Link to this type vertex_id()
vertex_id() :: non_neg_integer

Link to this section Functions

Link to this function a_star(g, a, b, hfun)
a_star(t, vertex, vertex, (vertex, vertex -> integer)) :: [vertex]

Gets the shortest path between a and b.

The A algorithm is very much like Dijkstra’s algorithm, except in addition to edge weights, A also considers a heuristic function for determining the lower bound of the cost to go from vertex v to b. The lower bound must be less than the cost of the shortest path from v to b, otherwise it will do more harm than good. Dijkstra’s algorithm can be reframed as A* where lower_bound(v) is always 0.

This function puts the heuristics in your hands, so you must provide the heuristic function, which should take a single parameter, v, which is the vertex being currently examined. Your heuristic should then determine what the lower bound for the cost to reach b from v is, and return that value.

Example

iex> g = Graph.new |> Graph.add_edges([{:a, :b}, {:b, :c}, {:c, :d}, {:b, :d}])
...> Graph.a_star(g, :a, :d, fn _ -> 0 end)
[:a, :b, :d]

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :c}, {:b, :c}, {:b, :d}])
...> Graph.a_star(g, :a, :d, fn _ -> 0 end)
nil
Link to this function add_edge(g, edge)
add_edge(t, Graph.Edge.t) :: t

Like add_edge/3 or add_edge/4, but takes a Graph.Edge struct created with Graph.Edge.new/2 or Graph.Edge.new/3.

Example

iex> g = Graph.new |> Graph.add_edge(Graph.Edge.new(:a, :b))
...> [:a, :b] = Graph.vertices(g)
...> Graph.edges(g)
[%Graph.Edge{v1: :a, v2: :b}]
Link to this function add_edge(g, a, b, opts \\ [])
add_edge(t, vertex, vertex, Graph.Edge.edge_opts) ::
  t |
  {:error, {:invalid_edge_option, term}}

Adds an edge connecting a to b. If either a or b do not exist in the graph, they are automatically added. Adding the same edge more than once does not create multiple edges, each edge is only ever stored once.

Edges have a default weight of 1, and an empty (nil) label. You can change this by passing options to this function, as shown below.

Example

iex> g = Graph.new |> Graph.add_edge(:a, :b)
...> [:a, :b] = Graph.vertices(g)
...> Graph.edges(g)
[%Graph.Edge{v1: :a, v2: :b, label: nil, weight: 1}]

iex> g = Graph.new |> Graph.add_edge(:a, :b, label: :foo, weight: 2)
...> [:a, :b] = Graph.vertices(g)
...> Graph.edges(g)
[%Graph.Edge{v1: :a, v2: :b, label: :foo, weight: 2}]
Link to this function add_edges(g, es)
add_edges(t, [Graph.Edge.t]) ::
  t |
  {:error, {:invalid_edge, term}}

Like add_edge/3, but takes a list of Graph.Edge structs, and adds an edge to the graph for each pair.

See the docs for Graph.Edge.new/2 or Graph.Edge.new/3 for more info.

Examples

iex> alias Graph.Edge
...> edges = [Edge.new(:a, :b), Edge.new(:b, :c, weight: 2)]
...> g = Graph.new |> Graph.add_vertices([:a, :b, :c]) |> Graph.add_edges(edges)
...> Graph.edges(g)
[%Graph.Edge{v1: :a, v2: :b}, %Graph.Edge{v1: :b, v2: :c, weight: 2}]

iex> Graph.new |> Graph.add_vertices([:a, :b, :c]) |> Graph.add_edges([:a, :b])
{:error, {:invalid_edge, :a}}
Link to this function add_vertex(g, v, label \\ nil)

Adds a new vertex to the graph. If the vertex is already present in the graph, the add is a no-op.

You can provide an optional label for the vertex, aside from the variety of uses this has for working with graphs, labels will also be used when exporting a graph in DOT format.

Example

iex> g = Graph.new |> Graph.add_vertex(:a, :mylabel) |> Graph.add_vertex(:a)
...> [:a] = Graph.vertices(g)
...> Graph.vertex_label(g, :a)
:mylabel
Link to this function add_vertices(g, vs)
add_vertices(t, [vertex]) :: t

Like add_vertex/2, but takes a list of vertices to add to the graph.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :a])
...> Graph.vertices(g)
[:a, :b]
Link to this function arborescence_root(g)
arborescence_root(t) :: vertex | nil

Returns the root vertex of the arborescence, if one exists, otherwise nil.

Link to this function components(g)
components(t) :: [[vertex]]

Returns a list of connected components, where each component is a list of vertices.

A connected component is a maximal subgraph such that there is a path between each pair of vertices, considering all edges undirected.

A subgraph is a graph whose vertices and edges are a subset of the vertices and edges of the source graph.

A maximal subgraph is a subgraph with property P where all other subgraphs which contain the same vertices do not have that same property P.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :b}, {:a, :c}, {:b, :c}, {:c, :d}, {:c, :a}])
...> Graph.components(g)
[[:d, :b, :c, :a]]
Link to this function delete_edge(g, a, b)

Removes an edge connecting a to b. If no such vertex exits, or the edge does not exist, it is effectively a no-op.

Example

iex> g = Graph.new |> Graph.add_edge(:a, :b) |> Graph.delete_edge(:a, :b)
...> [:a, :b] = Graph.vertices(g)
...> Graph.edges(g)
[]
Link to this function delete_edges(g, es)
delete_edges(t, [{vertex, vertex}]) ::
  t |
  {:error, {:invalid_edge, term}}

Like delete_edge/3, but takes a list of vertex pairs, and deletes the corresponding edge from the graph, if it exists.

Examples

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c]) |> Graph.add_edge(:a, :b)
...> g = Graph.delete_edges(g, [{:a, :b}])
...> Graph.edges(g)
[]

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c]) |> Graph.add_edge(:a, :b)
...> Graph.delete_edges(g, [:a])
{:error, {:invalid_edge, :a}}
Link to this function delete_vertex(g, v)
delete_vertex(t, vertex) :: t

Removes a vertex from the graph, as well as any edges which refer to that vertex. If the vertex does not exist in the graph, it is a no-op.

Example

iex> g = Graph.new |> Graph.add_vertex(:a) |> Graph.add_vertex(:b) |> Graph.add_edge(:a, :b)
...> [:a, :b] = Graph.vertices(g)
...> [%Graph.Edge{v1: :a, v2: :b}] = Graph.edges(g)
...> g = Graph.delete_vertex(g, :b)
...> [:a] = Graph.vertices(g)
...> Graph.edges(g)
[]
Link to this function delete_vertices(g, vs)
delete_vertices(t, [vertex]) :: t

Like delete_vertex/2, but takes a list of vertices to delete from the graph.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c]) |> Graph.delete_vertices([:a, :b])
...> Graph.vertices(g)
[:c]
Link to this function dijkstra(g, a, b)
dijkstra(t, vertex, vertex) :: [vertex]

Gets the shortest path between a and b.

As indicated by the name, this uses Dijkstra’s algorithm for locating the shortest path, which means that edge weights are taken into account when determining which vertices to search next. By default, all edges have a weight of 1, so vertices are inspected at random; which causes this algorithm to perform a naive depth-first search of the graph until a path is found. If your edges are weighted however, this will allow the algorithm to more intelligently navigate the graph.

Example

iex> g = Graph.new |> Graph.add_edges([{:a, :b}, {:b, :c}, {:c, :d}, {:b, :d}])
...> Graph.dijkstra(g, :a, :d)
[:a, :b, :d]

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :c}, {:b, :c}, {:b, :d}])
...> Graph.dijkstra(g, :a, :d)
nil
Link to this function edge_label(graph, v1, v2)
edge_label(t, vertex, vertex) :: term | nil

Returns the label for the given vertex. If no label was assigned, it returns nil.

Example

iex> g = Graph.new |> Graph.add_edge(:a, :b, label: :my_edge)
...> Graph.edge_label(g, :a, :b)
:my_edge
Link to this function edges(graph)
edges(t) :: [Graph.Edge.t]

Return a list of all the edges, where each edge is expressed as a tuple of {A, B}, where the elements are the vertices involved, and implying the direction of the edge to be from A to B.

NOTE: You should be careful when using this on dense graphs, as it produces lists with whatever you’ve provided as vertices, with likely many copies of each. I’m not sure if those copies are shared in-memory as they are unchanged, so it should be fairly compact in memory, but I have not verified that to be sure.

Example

iex> g = Graph.new |> Graph.add_vertex(:a) |> Graph.add_vertex(:b) |> Graph.add_vertex(:c)
...> g = g |> Graph.add_edge(:a, :c) |> Graph.add_edge(:b, :c)
...> Graph.edges(g)
[%Graph.Edge{v1: :a, v2: :c}, %Graph.Edge{v1: :b, v2: :c}]
Link to this function get_paths(g, a, b)
get_paths(t, vertex, vertex) :: [[vertex]]

Builds a list of paths between vertex a and vertex b.

The algorithm used here is a depth-first search, which evaluates the whole graph until all paths are found. Order is guaranteed to be deterministic, but not guaranteed to be in any meaningful order (i.e. shortest to longest).

Example

iex> g = Graph.new |> Graph.add_edges([{:a, :b}, {:b, :c}, {:c, :d}, {:b, :d}, {:c, :a}])
...> Graph.get_paths(g, :a, :d)
[[:a, :b, :c, :d], [:a, :b, :d]]

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :c}, {:b, :c}, {:b, :d}])
...> Graph.get_paths(g, :a, :d)
[]
Link to this function get_shortest_path(g, a, b)
get_shortest_path(t, vertex, vertex) :: [vertex]

See dijkstra/1.

Link to this function has_vertex?(graph, v)
has_vertex?(t, vertex) :: boolean

Returns true if the given vertex exists in the graph. Otherwise false.

Link to this function in_degree(g, v)

Returns the in-degree of vertex v of graph g.

The in-degree of a vertex is the number of edges directed inbound towards that vertex.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c]) |> Graph.add_edge(:a, :b)
...> Graph.in_degree(g, :b)
1
Link to this function in_edges(g, v)
in_edges(t, vertex) :: Graph.Edge.t

Returns a list of Graph.Edge structs representing the in edges to vertex v.

Link to this function in_neighbors(g, v)
in_neighbors(t, vertex) :: [vertex]

Returns a list of vertices which all have edges coming in to the given vertex v.

Link to this function info(g)
info(t) :: %{num_edges: non_neg_integer, num_vertices: non_neg_integer}

Returns a map of summary information about this graph.

NOTE: The size_in_bytes value is an estimate, not a perfectly precise value, but should be close enough to be useful.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = g |> Graph.add_edges([{:a, :b}, {:b, :c}])
...> Graph.info(g)
%{num_vertices: 4, num_edges: 2, size_in_bytes: 952}
Link to this function is_acyclic?(g)
is_acyclic?(t) :: boolean

Returns true if and only if the graph g is acyclic.

Link to this function is_arborescence?(g)
is_arborescence?(t) :: boolean

Returns true if the graph is an aborescence, a directed acyclic graph, where the root, a vertex, of the arborescence has a unique path from itself to every other vertex in the graph.

Link to this function is_cyclic?(g)
is_cyclic?(t) :: boolean

Returns true if the graph g is not acyclic.

Link to this function is_subgraph?(graph1, graph2)
is_subgraph?(t, t) :: boolean

Returns true if graph g1 is a subgraph of g2.

A graph is a subgraph of another graph if it’s vertices and edges are a subset of that graph’s vertices and edges.

Example

iex> g1 = Graph.new |> Graph.add_vertices([:a, :b, :c, :d]) |> Graph.add_edge(:a, :b) |> Graph.add_edge(:b, :c)
...> g2 = Graph.new |> Graph.add_vertices([:b, :c]) |> Graph.add_edge(:b, :c)
...> Graph.is_subgraph?(g2, g1)
true
Link to this function is_tree?(g)
is_tree?(t) :: boolean

Returns true if and only if the graph g is a tree.

Link to this function label_vertex(g, v, label)
label_vertex(t, vertex, term) ::
  t |
  {:error, {:invalid_vertex, vertex}}

Updates the label for the given vertex.

If no such vertex exists in the graph, {:error, {:invalid_vertex, v}} is returned.

Example

iex> g = Graph.new |> Graph.add_vertex(:a, :foo)
...> :foo = Graph.vertex_label(g, :a)
...> g = Graph.label_vertex(g, :a, :bar)
...> Graph.vertex_label(g, :a)
:bar
Link to this function loop_vertices(g)
loop_vertices(t) :: [vertex]

Returns a list of vertices from graph g which are included in a loop, where a loop is a cycle of length 1.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c]) |> Graph.add_edge(:a, :a)
...> Graph.loop_vertices(g)
[:a]
Link to this function new()
new() :: t

Creates a new graph.

Link to this function num_edges(graph)
num_edges(t) :: non_neg_integer

Returns the number of edges in the graph

Example

iex> g = Graph.add_edges(Graph.new, [{:a, :b}, {:b, :c}, {:a, :a}])
...> Graph.num_edges(g)
3
Link to this function num_vertices(graph)
num_vertices(t) :: non_neg_integer

Returns the number of vertices in the graph

Example

iex> g = Graph.add_vertices(Graph.new, [:a, :b, :c])
...> Graph.num_vertices(g)
3
Link to this function out_degree(g, v)
out_degree(t, vertex) :: non_neg_integer

Returns the out-degree of vertex v of graph g.

The out-degree of a vertex is the number of edges directed outbound from that vertex.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c]) |> Graph.add_edge(:a, :b)
...> Graph.out_degree(g, :a)
1
Link to this function out_edges(g, v)
out_edges(t, vertex) :: Graph.Edge.t

Returns a list of Graph.Edge structs representing the out edges from vertex v.

Link to this function out_neighbors(g, v)
out_neighbors(t, vertex) :: [vertex]

Returns a list of vertices which the given vertex v has edges going to.

Link to this function postorder(g)
postorder(t) :: [vertex]

Returns all vertices of graph g. The order is given by a depth-first traversal of the graph, collecting visited vertices in postorder. More precisely, the vertices visited while searching from an arbitrarily chosen vertex are collected in postorder, and all those collected vertices are placed before the subsequently visited vertices.

Example

Our example code constructs a graph which looks like so:

    :a
                 :b
      /           :c   :d
    /
   :e

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d, :e])
...> g = Graph.add_edges(g, [{:a, :b}, {:b, :c}, {:b, :d}, {:c, :e}])
...> Graph.postorder(g)
[:e, :c, :d, :b, :a]
Link to this function preorder(g)
preorder(t) :: [vertex]

Returns all vertices of graph g. The order is given by a depth-first traversal of the graph, collecting visited vertices in preorder.

Example

Our example code constructs a graph which looks like so:

     :a
                   :b
       /           :c   :d
     /
   :e

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d, :e])
...> g = Graph.add_edges(g, [{:a, :b}, {:b, :c}, {:b, :d}, {:c, :e}])
...> Graph.preorder(g)
[:a, :b, :c, :e, :d]
Link to this function reachable(g, vs)
reachable(t, [vertex]) :: [[vertex]]

Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it v), there is a path in the graph from some vertex of vs to v.

As paths of length zero are allowed, the vertices of vs are also included in the returned list.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :b}, {:a, :c}, {:b, :c}, {:c, :d}])
...> Graph.reachable(g, [:a])
[:d, :c, :b, :a]
Link to this function reachable_neighbors(g, vs)
reachable_neighbors(t, [vertex]) :: [[vertex]]

Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it v), there is a path in the graph of length one or more from some vertex of vs to v.

As a consequence, only those vertices of vs that are included in some cycle are returned.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :b}, {:a, :c}, {:b, :c}, {:c, :d}])
...> Graph.reachable_neighbors(g, [:a])
[:d, :c, :b]
Link to this function reaching(g, vs)
reaching(t, [vertex]) :: [[vertex]]

Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it v), there is a path from v to some vertex of vs.

As paths of length zero are allowed, the vertices of vs are also included in the returned list.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :b}, {:a, :c}, {:b, :c}, {:c, :d}])
...> Graph.reaching(g, [:d])
[:b, :a, :c, :d]
Link to this function reaching_neighbors(g, vs)
reaching_neighbors(t, [vertex]) :: [[vertex]]

Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it v), there is a path of length one or more from v to some vertex of vs.

As a consequence, only those vertices of vs that are included in some cycle are returned.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d]) …> g = Graph.add_edges(g, [{:a, :b}, {:a, :c}, {:b, :c}, {:c, :a}, {:b, :d}]) …> Graph.reaching_neighbors(g, [:b]) [:b, :c, :a]

Link to this function replace_vertex(g, v, rv)
replace_vertex(t, vertex, vertex) ::
  t |
  {:error, :no_such_vertex}

Replaces vertex with new_vertex in the graph.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b]) |> Graph.add_edge(:a, :b)
...> [:a, :b] = Graph.vertices(g)
...> g = Graph.replace_vertex(g, :a, :c)
...> [:b, :c] = Graph.vertices(g)
...> Graph.edges(g)
[%Graph.Edge{v1: :c, v2: :b}]
Link to this function split_edge(g, v1, v2, v3)
split_edge(t, vertex, vertex, vertex) ::
  t |
  {:error, :no_such_edge}

Splits the edge between v1 and v2 by inserting a new vertex, v3, deleting the edge between v1 and v2, and inserting an edge from v1 to v3 and from v3 to v2.

The two resulting edges from the split will share the same weight and label.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :c]) |> Graph.add_edge(:a, :c, weight: 2)
...> g = Graph.split_edge(g, :a, :c, :b)
...> Graph.edges(g)
[%Graph.Edge{v1: :a, v2: :b, weight: 2}, %Graph.Edge{v1: :b, v2: :c, weight: 2}]
Link to this function strong_components(g)
strong_components(t) :: [[vertex]]

Returns a list of strongly connected components, where each component is a list of vertices.

A strongly connected component is a maximal subgraph such that there is a path between each pair of vertices.

See components/1 for the definitions of subgraph and maximal subgraph if you are unfamiliar with the terminology.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :b}, {:a, :c}, {:b, :c}, {:c, :d}, {:c, :a}])
...> Graph.strong_components(g)
[[:d], [:b, :c, :a]]
Link to this function subgraph(graph, vs)
subgraph(t, [vertex]) :: t

Builds a maximal subgraph of g which includes all of the vertices in vs and the edges which connect them.

See the test suite for example usage.

Link to this function to_dot(g)
to_dot(t) :: {:ok, binary} | {:error, term}

Converts the given Graph to DOT format, which can then be converted to a number of other formats via Graphviz, e.g. dot -Tpng out.dot > out.png.

If labels are set on a vertex, then those labels are used in the DOT output in place of the vertex itself. If no labels were set, then the vertex is stringified if it’s a primitive type and inspected if it’s not, in which case the inspect output will be quoted and used as the vertex label in the DOT file.

Edge labels and weights will be shown as attributes on the edge definitions, otherwise they use the same labelling scheme for the involved vertices as described above.

NOTE: Currently this function assumes graphs are directed graphs, but in the future it will support undirected graphs as well.

Example

> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
> g = Graph.add_edges([{:a, :b}, {:b, :c}, {:b, :d}, {:c, :d}])
> g = Graph.label_vertex(g, :a, :start)
> g = Graph.label_vertex(g, :d, :finish)
> g = Graph.update_edge(g, :b, :d, weight: 3)
> IO.puts(Graph.to_dot(g))
strict digraph {
    start
    b
    c
    finish
    start -> b
    b -> c
    b -> finish [weight=3]
    c -> finish
}
Link to this function topsort(g)
topsort(t) :: [vertex]

Returns a topological ordering of the vertices of graph g, if such an ordering exists, otherwise it returns false. For each vertex in the returned list, no out-neighbors occur earlier in the list.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :b}, {:a, :c}, {:b, :c}, {:c, :d}])
...> Graph.topsort(g)
[:a, :b, :c, :d]

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c, :d])
...> g = Graph.add_edges(g, [{:a, :b}, {:a, :c}, {:b, :c}, {:c, :d}, {:c, :a}])
...> Graph.topsort(g)
false
Link to this function transpose(g)
transpose(t) :: t

The transposition of a graph is another graph with the direction of all the edges reversed.

Example

iex> g = Graph.new |> Graph.add_vertices([:a, :b, :c]) |> Graph.add_edge(:a, :b) |> Graph.add_edge(:b, :c)
...> g |> Graph.transpose |> Graph.edges
[%Graph.Edge{v1: :b, v2: :a}, %Graph.Edge{v1: :c, v2: :b}]
Link to this function update_edge(g, v1, v2, opts)
update_edge(t, vertex, vertex, Graph.Edge.edge_opts) ::
  t |
  {:error, :no_such_edge}

Updates the metadata (weight/label) for an edge using the provided options.

Example

iex> g = Graph.new |> Graph.add_edge(:a, :b)
...> [%Graph.Edge{v1: :a, v2: :b, label: nil, weight: 1}] = Graph.edges(g)
...> %Graph{} = g = Graph.update_edge(g, :a, :b, weight: 2, label: :foo)
...> Graph.edges(g)
[%Graph.Edge{v1: :a, v2: :b, label: :foo, weight: 2}]
Link to this function vertex_label(graph, v)
vertex_label(t, vertex) :: term | nil

Returns the label for the given vertex. If no label was assigned, it returns nil.

Example

iex> g = Graph.new |> Graph.add_vertex(:a) |> Graph.label_vertex(:a, :my_label)
...> Graph.vertex_label(g, :a)
:my_label
Link to this function vertices(graph)
vertices(t) :: vertex

Returns a list of all the vertices in the graph.

NOTE: You should be careful when using this on large graphs, as the list it produces contains every vertex on the graph. I have not yet verified whether Erlang ensures that they are a shared reference with the original, or copies, but if the latter it could result in running out of memory if the graph is too large.

Example

iex> g = Graph.new |> Graph.add_vertex(:a) |> Graph.add_vertex(:b)
...> Graph.vertices(g)
[:a, :b]