Specs

add_edge(G, V1, V2) -> edge() | {error, add_edge_err_rsn()}
            when G :: graph(), V1 :: vertex(), V2 :: vertex().

add_edge/5 creates (or modifies) edge E of digraph G, using Label as the (new) label of the edge. The edge is emanating from V1 and incident on V2. Returns E.

add_edge(G, V1, V2, Label) is equivalent to add_edge(G, E, V1, V2, Label), where E is a created edge. The created edge is represented by term ['$e' | N], where N is an integer >= 0.

add_edge(G, V1, V2) is equivalent to add_edge(G, V1, V2, []).

If the edge would create a cycle in an acyclic digraph, {error, {bad_edge, Path}} is returned. If G already has an edge with value E connecting a different pair of vertices, {error, {bad_edge, [V1, V2]}} is returned. If either of V1 or V2 is not a vertex of digraph G, {error, {bad_vertex, V}} is returned, V = V1 or V = V2.

Specs

add_edge(G, V1, V2, Label) -> edge() | {error, add_edge_err_rsn()}
            when G :: graph(), V1 :: vertex(), V2 :: vertex(), Label :: label().

Specs

add_edge(G, E, V1, V2, Label) -> edge() | {error, add_edge_err_rsn()}
            when G :: graph(), E :: edge(), V1 :: vertex(), V2 :: vertex(), Label :: label().

Specs

add_vertex(G) -> vertex() when G :: graph().

add_vertex/3 creates (or modifies) vertex V of digraph G, using Label as the (new) label of the vertex. Returns V.

add_vertex(G, V) is equivalent to add_vertex(G, V, []).

add_vertex/1 creates a vertex using the empty list as label, and returns the created vertex. The created vertex is represented by term ['$v' | N], where N is an integer >= 0.

Specs

add_vertex(G, V) -> vertex() when G :: graph(), V :: vertex().

Specs

add_vertex(G, V, Label) -> vertex() when G :: graph(), V :: vertex(), Label :: label().

Specs

del_edge(G, E) -> true when G :: graph(), E :: edge().

Deletes edge E from digraph G.

Specs

del_edges(G, Edges) -> true when G :: graph(), Edges :: [edge()].

Deletes the edges in list Edges from digraph G.

Specs

del_path(G, V1, V2) -> true when G :: graph(), V1 :: vertex(), V2 :: vertex().

Deletes edges from digraph G until there are no paths from vertex V1 to vertex V2.

A sketch of the procedure employed:

• Find an arbitrary simple path v[1], v[2], ..., v[k] from V1 to V2 in G.

• Remove all edges of G emanating from v[i] and incident to v[i+1] for 1 <= i < k (including multiple edges).

• Repeat until there is no path between V1 and V2.

Specs

del_vertex(G, V) -> true when G :: graph(), V :: vertex().

Deletes vertex V from digraph G. Any edges emanating from V or incident on V are also deleted.

Specs

del_vertices(G, Vertices) -> true when G :: graph(), Vertices :: [vertex()].

Deletes the vertices in list Vertices from digraph G.

Specs

delete(G) -> true when G :: graph().

Deletes digraph G. This call is important as digraphs are implemented with ETS. There is no garbage collection of ETS tables. However, the digraph is deleted if the process that created the digraph terminates.

Specs

edge(G, E) -> {E, V1, V2, Label} | false
        when G :: graph(), E :: edge(), V1 :: vertex(), V2 :: vertex(), Label :: label().

Returns {E, V1, V2, Label}, where Label is the label of edge E emanating from V1 and incident on V2 of digraph G. If no edge E of digraph G exists, false is returned.

Specs

edges(G) -> Edges when G :: graph(), Edges :: [edge()].

Returns a list of all edges of digraph G, in some unspecified order.

Specs

edges(G, V) -> Edges when G :: graph(), V :: vertex(), Edges :: [edge()].

Returns a list of all edges emanating from or incident on V of digraph G, in some unspecified order.

Specs

get_cycle(G, V) -> Vertices | false when G :: graph(), V :: vertex(), Vertices :: [vertex(), ...].

If a simple cycle of length two or more exists through vertex V, the cycle is returned as a list [V, ..., V] of vertices. If a loop through V exists, the loop is returned as a list [V]. If no cycles through V exist, false is returned.

get_path/3 is used for finding a simple cycle through V.

Specs

get_path(G, V1, V2) -> Vertices | false
            when G :: graph(), V1 :: vertex(), V2 :: vertex(), Vertices :: [vertex(), ...].

Tries to find a simple path from vertex V1 to vertex V2 of digraph G. Returns the path as a list [V1, ..., V2] of vertices, or false if no simple path from V1 to V2 of length one or more exists.

Digraph G is traversed in a depth-first manner, and the first found path is returned.

Specs

get_short_cycle(G, V) -> Vertices | false
                   when G :: graph(), V :: vertex(), Vertices :: [vertex(), ...].

Tries to find an as short as possible simple cycle through vertex V of digraph G. Returns the cycle as a list [V, ..., V] of vertices, or false if no simple cycle through V exists. Notice that a loop through V is returned as list [V, V].

get_short_path/3 is used for finding a simple cycle through V.

Specs

get_short_path(G, V1, V2) -> Vertices | false
                  when G :: graph(), V1 :: vertex(), V2 :: vertex(), Vertices :: [vertex(), ...].

Tries to find an as short as possible simple path from vertex V1 to vertex V2 of digraph G. Returns the path as a list [V1, ..., V2] of vertices, or false if no simple path from V1 to V2 of length one or more exists.

Digraph G is traversed in a breadth-first manner, and the first found path is returned.

Specs

in_degree(G, V) -> non_neg_integer() when G :: graph(), V :: vertex().

Returns the in-degree of vertex V of digraph G.

Specs

in_edges(G, V) -> Edges when G :: graph(), V :: vertex(), Edges :: [edge()].

Returns a list of all edges incident on V of digraph G, in some unspecified order.

Specs

in_neighbours(G, V) -> Vertex when G :: graph(), V :: vertex(), Vertex :: [vertex()].

Returns a list of all in-neighbors of V of digraph G, in some unspecified order.

Specs

info(G) -> InfoList
        when
            G :: graph(),
            InfoList ::
                [{cyclicity, Cyclicity :: d_cyclicity()} |
                 {memory, NoWords :: non_neg_integer()} |
                 {protection, Protection :: d_protection()}].

Returns a list of {Tag, Value} pairs describing digraph G. The following pairs are returned:

• {cyclicity, Cyclicity}, where Cyclicity is cyclic or acyclic, according to the options given to new.

• {memory, NoWords}, where NoWords is the number of words allocated to the ETS tables.

• {protection, Protection}, where Protection is protected or private, according to the options given to new.

Specs

new() -> graph().

Equivalent to new([]).

Specs

new(Type) -> graph() when Type :: [d_type()].

Returns an empty digraph with properties according to the options in Type:

cyclic

Allows cycles in the digraph (default).

acyclic

The digraph is to be kept acyclic.

protected

Other processes can read the digraph (default).

private

The digraph can be read and modified by the creating process only.

If an unrecognized type option T is specified or Type is not a proper list, a badarg exception is raised.

Specs

no_edges(G) -> non_neg_integer() when G :: graph().

Returns the number of edges of digraph G.

Specs

no_vertices(G) -> non_neg_integer() when G :: graph().

Returns the number of vertices of digraph G.

Specs

out_degree(G, V) -> non_neg_integer() when G :: graph(), V :: vertex().

Returns the out-degree of vertex V of digraph G.

Specs

out_edges(G, V) -> Edges when G :: graph(), V :: vertex(), Edges :: [edge()].

Returns a list of all edges emanating from V of digraph G, in some unspecified order.

Specs

out_neighbours(G, V) -> Vertices when G :: graph(), V :: vertex(), Vertices :: [vertex()].

Returns a list of all out-neighbors of V of digraph G, in some unspecified order.

Specs

vertex(G, V) -> {V, Label} | false when G :: graph(), V :: vertex(), Label :: label().

Returns {V, Label}, where Label is the label of the vertex V of digraph G, or false if no vertex V of digraph G exists.

Specs

vertices(G) -> Vertices when G :: graph(), Vertices :: [vertex()].

Returns a list of all vertices of digraph G, in some unspecified order.