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Module type Sig.G

module type G = sig .. end

Common signature for all graphs.

Graph structure

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.

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

Degree of a vertex

val out_degree : t -> vertex -> int

out_degree g v returns the out-degree of v in g.

val in_degree : t -> vertex -> int

in_degree g v returns the in-degree of v 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.

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

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

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.

val pred : t -> vertex -> vertex list

pred g v returns the predecessors of v in g.

Labeled edges going from/to a vertex

val succ_e : t -> vertex -> edge list

succ_e g v returns the edges going from v in g.

val pred_e : t -> vertex -> edge list

pred_e g v returns the edges going to v 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.

Time complexity for ocamlgraph implementations: 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.

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

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

iter/fold on all edges going from/to a vertex.

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