Module Pack.Graph

module Graph: Sig_pack.S 
Undirected imperative graphs with edges and vertices labeled with integer.


Graph structure


type t 
abstract type of graphs
module V: sig .. end
Vertices
type vertex = V.t 
module E: sig .. end
Edges
type edge = E.t 
val is_directed : bool
is this an implementation of directed graphs?

Graph constructors and destructors


val create : ?size:int -> unit -> t
Return an empty graph. Optionally, a size can be given, which should be on the order of the expected number of vertices that will be in the graph (for hash tables-based implementations). The graph grows as needed, so size is just an initial guess.
val clear : t -> unit
Remove all vertices and edges from the given graph.
Since ocamlgraph 1.4
val copy : t -> t
copy g returns a copy of g. Vertices and edges (and eventually marks, see module Mark) are duplicated.
val add_vertex : t -> V.t -> unit
add_vertex g v adds the vertex v from the graph g. Do nothing if v is already in g.
val remove_vertex : t -> V.t -> unit
remove g v removes the vertex v from the graph g (and all the edges going from v in g). Do nothing if v is not in g.
val add_edge : t -> V.t -> V.t -> unit
add_edge g v1 v2 adds an edge from the vertex v1 to the vertex v2 in the graph g. Add also v1 (resp. v2) in g if v1 (resp. v2) is not in g. Do nothing if this edge is already in g.
val add_edge_e : t -> E.t -> unit
add_edge_e g e adds the edge e in the graph g. Add also E.src e (resp. E.dst e) in g if E.src e (resp. E.dst e) is not in g. Do nothing if e is already in g.
val remove_edge : t -> V.t -> V.t -> unit
remove_edge g v1 v2 removes the edge going from v1 to v2 from the graph g. Do nothing if this edge is not in g.
Raises Invalid_argument if v1 or v2 are not in g.
val remove_edge_e : t -> E.t -> unit
remove_edge_e g e removes the edge e from the graph g. Do nothing if e is not in g.
Raises Invalid_argument if E.src e or E.dst e are not in g.
module Mark: sig .. end
Vertices contains integers marks, which can be set or used by some algorithms (see for instance module Marking below)

Size functions


val is_empty : t -> bool
val nb_vertex : t -> int
val nb_edges : t -> int

Degree of a vertex
val out_degree : t -> V.t -> int
out_degree g v returns the out-degree of v in g.
Raises Invalid_argument if v is not in g.
val in_degree : t -> V.t -> int
in_degree g v returns the in-degree of v in g.
Raises Invalid_argument if v is not in g.

Membership functions


val mem_vertex : t -> V.t -> bool
val mem_edge : t -> V.t -> V.t -> bool
val mem_edge_e : t -> E.t -> bool
val find_edge : t -> V.t -> V.t -> E.t
val find_all_edges : t -> V.t -> V.t -> E.t list

Successors and predecessors of a vertex


val succ : t -> V.t -> V.t list
succ g v returns the successors of v in g.
Raises Invalid_argument if v is not in g.
val pred : t -> V.t -> V.t list
pred g v returns the predecessors of v in g.
Raises Invalid_argument if v is not in g.

Labeled edges going from/to a vertex
val succ_e : t -> V.t -> E.t list
succ_e g v returns the edges going from v in g.
Raises Invalid_argument if v is not in g.
val pred_e : t -> V.t -> E.t list
pred_e g v returns the edges going to v in g.
Raises Invalid_argument if v is not in g.

Graph iterators



iter/fold on all vertices/edges of a graph
val iter_vertex : (V.t -> unit) -> t -> unit
val iter_edges : (V.t -> V.t -> unit) -> t -> unit
val fold_vertex : (V.t -> 'a -> 'a) -> t -> 'a -> 'a
val fold_edges : (V.t -> V.t -> 'a -> 'a) -> t -> 'a -> 'a
val map_vertex : (V.t -> V.t) -> t -> t
map iterator on vertex

iter/fold on all labeled edges of a graph
val iter_edges_e : (E.t -> unit) -> t -> unit
val fold_edges_e : (E.t -> 'a -> 'a) -> t -> 'a -> 'a

Vertex iterators

Each iterator iterator f v g iters f to the successors/predecessors of v in the graph g and raises Invalid_argument if v is not in g.

iter/fold on all successors/predecessors of a vertex.

val iter_succ : (V.t -> unit) -> t -> V.t -> unit
val iter_pred : (V.t -> unit) -> t -> V.t -> unit
val fold_succ : (V.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a
val fold_pred : (V.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a

iter/fold on all edges going from/to a vertex.
val iter_succ_e : (E.t -> unit) -> t -> V.t -> unit
val fold_succ_e : (E.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a
val iter_pred_e : (E.t -> unit) -> t -> V.t -> unit
val fold_pred_e : (E.t -> 'a -> 'a) -> t -> V.t -> 'a -> 'a

Basic operations


val find_vertex : t -> int -> V.t
vertex g i returns a vertex of label i in g. The behaviour is unspecified if g has several vertices with label i. Note: this function is inefficient (linear in the number of vertices); you should better keep the vertices as long as you create them.
val transitive_closure : ?reflexive:bool -> t -> t
transitive_closure ?reflexive g returns the transitive closure of g (as a new graph). Loops (i.e. edges from a vertex to itself) are added only if reflexive is true (default is false).
val add_transitive_closure : ?reflexive:bool -> t -> t
add_transitive_closure ?reflexive g replaces g by its transitive closure. Meaningless for persistent implementations (then acts as transitive_closure).
val transitive_reduction : ?reflexive:bool -> t -> t
transitive_reduction ?reflexive g returns the transitive reduction of g (as a new graph). Loops (i.e. edges from a vertex to itself) are removed only if reflexive is true (default is false).
val replace_by_transitive_reduction : ?reflexive:bool -> t -> t
replace_by_transitive_reduction ?reflexive g replaces g by its transitive reduction. Meaningless for persistent implementations (then acts as transitive_reduction).
val mirror : t -> t
mirror g returns a new graph which is the mirror image of g: each edge from u to v has been replaced by an edge from v to u. For undirected graphs, it simply returns a copy of g.
val complement : t -> t
complement g builds a new graph which is the complement of g: each edge present in g is not present in the resulting graph and vice-versa. Edges of the returned graph are unlabeled.
val intersect : t -> t -> t
intersect g1 g2 returns a new graph which is the intersection of g1 and g2: each vertex and edge present in g1 *and* g2 is present in the resulting graph.
val union : t -> t -> t
union g1 g2 returns a new graph which is the union of g1 and g2: each vertex and edge present in g1 *or* g2 is present in the resulting graph.

Traversal


module Dfs: sig .. end
Depth-first search
module Bfs: sig .. end
Breadth-first search
module Marking: sig .. end
Graph traversal with marking

Graph generators


module Classic: sig .. end
Classic graphs
module Rand: sig .. end
Random graphs
module Components: sig .. end
Strongly connected components

Classical algorithms


val shortest_path : t -> V.t -> V.t -> E.t list * int
Dijkstra's shortest path algorithm. Weights are the labels.
val ford_fulkerson : t ->
V.t -> V.t -> (E.t -> int) * int
Ford Fulkerson maximum flow algorithm
val goldberg : t ->
V.t -> V.t -> (E.t -> int) * int
Goldberg maximum flow algorithm
val bellman_ford : t -> V.t -> E.t list
bellman_ford g v finds a negative cycle from v, and returns it, or raises Not_found if there is no such cycle
module PathCheck: sig .. end
Path checking
module Topological: sig .. end
Topological order
val spanningtree : t -> E.t list
Kruskal algorithm

Input / Output


val dot_output : t -> string -> unit
DOT output in a file
val display_with_gv : t -> unit
Displays the given graph using the external tools "dot" and "gv" and returns when gv's window is closed
val parse_gml_file : string -> t
val parse_dot_file : string -> t
val print_gml : Format.formatter -> t -> unit
val print_gml_file : t -> string -> unit