Module `Graph.Abstract`

Abstract Imperative Unlabeled Graphs.

Parameters

V : Sig.ANY_TYPE

Signature

An imperative graph with marks is an imperative graph.

include Sig.I

An imperative graph is a graph.

include Sig.G

type t: Abstract type of graphs

module V : Sig.VERTEX: Vertices have type V.t and are labeled with type V.label (note that an implementation may identify the vertex with its label)

type vertex = V.t

module E : Sig.EDGE with type vertex = vertex: Edges have type E.t and are labeled with type E.label. src (resp. dst) returns the origin (resp. the destination) of a given edge.

type edge = E.t

val is_directed : bool: Is this an implementation of directed graphs?

Size functions

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

val out_degree : t -> vertex -> 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 -> vertex -> 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 -> vertex -> bool

val mem_edge : t -> vertex -> vertex -> bool

val mem_edge_e : t -> edge -> bool

val find_edge : t -> vertex -> vertex -> edge

find_edge g v1 v2 returns the edge from v1 to v2 if it exists. Unspecified behaviour if g has several edges from v1 to v2.

raises Not_found: if no such edge exists.

val find_all_edges : t -> vertex -> vertex -> edge list

find_all_edges g v1 v2 returns all the edges from v1 to v2.

since: ocamlgraph 1.8

Successors and predecessors

You should better use iterators on successors/predecessors (see Section "Vertex iterators").

val succ : t -> vertex -> vertex list

succ g v returns the successors of v in g.

raises Invalid_argument: if v is not in g.

val pred : t -> vertex -> vertex list

pred g v returns the predecessors of v in g.

raises Invalid_argument: if v is not in g.

val succ_e : t -> vertex -> edge 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 -> vertex -> edge list

pred_e g v returns the edges going to v in g.

raises Invalid_argument: if v is not in g.

Graph iterators

val iter_vertex : (vertex -> unit) -> t -> unit: Iter on all vertices of a graph.

val fold_vertex : (vertex -> 'a -> 'a) -> t -> 'a -> 'a: Fold on all vertices of a graph.

val iter_edges : (vertex -> vertex -> unit) -> t -> unit: Iter on all edges of a graph. Edge label is ignored.

val fold_edges : (vertex -> vertex -> 'a -> 'a) -> t -> 'a -> 'a: Fold on all edges of a graph. Edge label is ignored.

val iter_edges_e : (edge -> unit) -> t -> unit: Iter on all edges of a graph.

val fold_edges_e : (edge -> 'a -> 'a) -> t -> 'a -> 'a: Fold on all edges of a graph.

val map_vertex : (vertex -> vertex) -> t -> t: Map on all vertices of a graph.

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. It is the same for functions fold_* which use an additional accumulator.

<b>Time complexity for ocamlgraph implementations:</b> operations on successors are in O(1) amortized for imperative graphs and in O(ln(|V|)) for persistent graphs while operations on predecessors are in O(max(|V|,|E|)) for imperative graphs and in O(max(|V|,|E|)*ln|V|) for persistent graphs.

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

val iter_succ_e : (edge -> unit) -> t -> vertex -> unit
val fold_succ_e : (edge -> 'a -> 'a) -> t -> vertex -> 'a -> 'a
val iter_pred_e : (edge -> unit) -> t -> vertex -> unit
val fold_pred_e : (edge -> 'a -> 'a) -> t -> vertex -> 'a -> 'a

val create : ?⁠size:int -> unit -> t: create () returns 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 -> vertex -> unit: add_vertex g v adds the vertex v to the graph g. Do nothing if v is already in g.

val remove_vertex : t -> vertex -> 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.

<b>Time complexity for ocamlgraph implementations:</b> O(|V|*ln(D)) for unlabeled graphs and O(|V|*D) for labeled graphs. D is the maximal degree of the graph.

val add_edge : t -> vertex -> vertex -> 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 -> edge -> 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 -> vertex -> vertex -> unit

remove_edge g v1 v2 removes the edge going from v1 to v2 from the graph g. If the graph is labelled, all the edges going from v1 to v2 are removed from 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 -> edge -> 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.MARK with type graph = t and type vertex = vertex: Mark on vertices. Marks can be used if you want to store some information on vertices: it is more efficient to use marks than an external table.