module type S =`sig`

..`end`

`type `

graph

`type `

vertex

`type `

edge

`type `

edge_label

`val merge_vertex : ``graph -> vertex list -> graph`

If no element of

`vl`

belongs to `g`

then `merge_vertex g (v::vl)`

is the
graph `g`

. Otherwise the collection of vertices of ```
merge_vertex g
(v::vl)
```

is the collection of vertices of `g`

from which all the elements
of `vl`

were removed and to which `v`

was added. Any edge of ```
merge_vertex
g (v::vl)
```

is an edge of `g`

whose source (destination) was changed to `v`

if it belongs to `vl`

. The function `merge_vertex`

always returns a graph
with a smaller collection of vertices and a smaller collection of edges
(in the weak sense). However the labels appearing in ```
merge_vertex g
v::vl
```

are exactly the ones appearing in `g`

.`val merge_edges_e : ``?src:vertex ->`

?dst:vertex -> graph -> edge list -> graph

If no element of

`el`

belongs to `g`

then `merge_edges_e g (e::el)`

is the
graph `g`

. Otherwise the collection of vertices of ```
merge_edges_e g
(e::el)
```

is precisely the collection of vertices of `g`

from which the
sources and the destinations of all the elements of `el`

were removed and
to which the vertices `v`

and `w`

were added. If `dst`

was provided then
`v`

is `src`

otherwise it is the source of `e`

. If `dst`

was provided then
`w`

is `y`

otherwise it is the destination of `e`

. The collection of edges
of `merge_edges_e g e::el`

is precisely the collection of edges of `g`

from which all the elements of `el`

were removed and to which an edge from
`v`

to `w`

sharing the label of `e`

was added; the edges of `g`

being
understood up to the fact their source and destination were updated. Note
`v=w`

if and only if the source of some element of `el`

matches the
destination of some element of `el`

(possibly the same).`val merge_edges_with_label : ``?src:vertex ->`

?dst:vertex ->

?label:edge_label ->

graph -> edge_label -> graph

The graph

`merge_edges_with_label ?src ?tgt ?label g l`

is the graph
`merge_edges_e ?src ?dst g el`

with `el`

being the list of all edges of
`g`

carrying the label `l`

. If the optional value `label`

is provided then
the edge to which all the elements of `el`

are identified carries the
label `label`

. Otherwise it carries the label `l`

. In particular
`merge_edges_with_label ?src ?tgt ?label g l`

is the graph `g`

if and only
if there is at most one edge of `g`

carrying the label `l`

.`val merge_isolabelled_edges : ``graph -> graph`

The graph

`merge_isolabelled_edges g`

is obtained from `g`

by
identifying two vertices when they are the sources (destinations) of two
edges sharing the same label. Therefore two distinct edges of the
returned graph cannot carry the same label. In particular if all the
edges share the same label then the returned graph is either empty (if
`g`

is so) or a single vertex (if `g`

has no edge and at least one
vertex) or a single vertex and a single edge (if `g`

has both a vertex
and an edge). A label is carried by some edge of
`merge_isolabelled_edges g`

if and only if it is carried by some edge of
`g`

.`val merge_ends : ``?strict:bool ->`

?specified_vertex:vertex -> graph -> graph

A vertex

`v`

of `g`

is called an end if every edge of `g`

arriving to `v`

also starts from `v`

. It is called a strict end if no edge of `g`

arrives
to it. The graph `merge_ends g`

is the graph `merge_vertex vl`

where `vl`

is the list of (strict) ends of `g`

. The vertex substituted to the ends
can be specified.`val merge_starts : ``?strict:bool ->`

?specified_vertex:vertex -> graph -> graph

A vertex

`v`

of `g`

is called a start if every edge of `g`

starting from
`v`

also arrives to `v`

. It is called a strict start if no edge of `g`

starts from it. The graph `merge_starts g`

is the graph `merge_vertex vl`

where `vl`

is the list of (strict) starts of `g`

. The vertex substituted
to the starts can be specified.`val merge_scc : ``?loop_killer:bool ->`

?specified_vertex:(vertex list -> vertex) ->

graph -> graph

The vertex of every strongly connected component are identified. If the
option

`loop_killer`

is set to `true`

then all the edges between identified
vertices are removed. The option `specified_vertex`

allows to choose the
vertex that replaces the elements of a strongly connected component.