ugraphs.pl -- Graph manipulation library
The S-representation of a graph is a list of (vertex-neighbours) pairs, where the pairs are in standard order (as produced by keysort) and the neighbours of each vertex are also in standard order (as produced by sort). This form is convenient for many calculations.
A new UGraph from raw data can be created using vertices_edges_to_ugraph/3.
Adapted to support some of the functionality of the SICStus ugraphs library by Vitor Santos Costa.
Ported from YAP 5.0.1 to SWI-Prolog by Jan Wielemaker.
- vertices(+Graph, -Vertices)
- Unify Vertices with all vertices appearing in Graph. Example:
?- vertices([1-[3,5],2-[4],3-[],4-[5],5-[]], L). L = [1, 2, 3, 4, 5]
- vertices_edges_to_ugraph(+Vertices, +Edges, -UGraph) is det
- Create a UGraph from Vertices and edges. Given a graph with a
set of Vertices and a set of Edges, Graph must unify with the
corresponding S-representation. Note that the vertices without
edges will appear in Vertices but not in Edges. Moreover, it is
sufficient for a vertice to appear in Edges.
?- vertices_edges_to_ugraph([],[1-3,2-4,4-5,1-5], L). L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[]]
In this case all vertices are defined implicitly. The next example shows three unconnected vertices:
?- vertices_edges_to_ugraph([6,7,8],[1-3,2-4,4-5,1-5], L). L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[], 6-[], 7-[], 8-[]]
- add_vertices(+Graph, +Vertices, -NewGraph)
- Unify NewGraph with a new graph obtained by adding the list of
Vertices to Graph. Example:
?- add_vertices([1-[3,5],2-[]], [0,1,2,9], NG). NG = [0-[], 1-[3,5], 2-[], 9-[]]
- del_vertices(+Graph, +Vertices, -NewGraph) is det
- Unify NewGraph with a new graph obtained by deleting the list of
Vertices and all the edges that start from or go to a vertex in
Vertices to the Graph. Example:
?- del_vertices([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[2,6],8-[]], [2,1], NL). NL = [3-[],4-[5],5-[],6-[],7-[6],8-[]]
- add_edges(+Graph, +Edges, -NewGraph)
- Unify NewGraph with a new graph obtained by adding the list of Edges
to Graph. Example:
?- add_edges([1-[3,5],2-[4],3-[],4-[5], 5-[],6-[],7-[],8-[]], [1-6,2-3,3-2,5-7,3-2,4-5], NL). NL = [1-[3,5,6], 2-[3,4], 3-[2], 4-[5], 5-[7], 6-[], 7-[], 8-[]]
- ugraph_union(+Graph1, +Graph2, -NewGraph)
- NewGraph is the union of Graph1 and Graph2. Example:
?- ugraph_union([1-[2],2-[3]],[2-[4],3-[1,2,4]],L). L = [1-[2], 2-[3,4], 3-[1,2,4]]
- del_edges(+Graph, +Edges, -NewGraph)
- Unify NewGraph with a new graph obtained by removing the list of
Edges from Graph. Notice that no vertices are deleted. Example:
?- del_edges([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[],8-[]], [1-6,2-3,3-2,5-7,3-2,4-5,1-3], NL). NL = [1-[5],2-[4],3-[],4-[],5-[],6-[],7-[],8-[]]
- edges(+Graph, -Edges)
- Unify Edges with all edges appearing in Graph. Example:
?- edges([1-[3,5],2-[4],3-[],4-[5],5-[]], L). L = [1-3, 1-5, 2-4, 4-5]
- transitive_closure(+Graph, -Closure)
- Generate the graph Closure as the transitive closure of Graph.
Example:
?- transitive_closure([1-[2,3],2-[4,5],4-[6]],L). L = [1-[2,3,4,5,6], 2-[4,5,6], 4-[6]]
- transpose_ugraph(Graph, NewGraph) is det
- Unify NewGraph with a new graph obtained from Graph by replacing
all edges of the form V1-V2 by edges of the form V2-V1. The cost
is O(|V|*log(|V|)). Notice that an undirected graph is its own
transpose. Example:
?- transpose([1-[3,5],2-[4],3-[],4-[5], 5-[],6-[],7-[],8-[]], NL). NL = [1-[],2-[],3-[1],4-[2],5-[1,4],6-[],7-[],8-[]]
- compose(+LeftGraph, +RightGraph, -NewGraph)
- Compose NewGraph by connecting the drains of LeftGraph to the
sources of RightGraph. Example:
?- compose([1-[2],2-[3]],[2-[4],3-[1,2,4]],L). L = [1-[4], 2-[1,2,4], 3-[]]
- ugraph_layers(Graph, -Layers) is semidet
- top_sort(+Graph, -Sorted) is semidet
- Sort vertices topologically. Layers is a list of lists of vertices
where there are no edges from a layer to an earlier layer. The
predicate top_sort/2 flattens the layers using append/2.
These predicates fail if Graph is cyclic. If Graph is not connected, the sub-graphs are individually sorted, where the root of each subgraph is in the first layer, the nodes connected to the roots in the second, etc.
?- top_sort([1-[2], 2-[3], 3-[]], L). L = [1, 2, 3]
- neighbors(+Vertex, +Graph, -Neigbours) is det
- neighbours(+Vertex, +Graph, -Neigbours) is det
- Neigbours is a sorted list of the neighbours of Vertex in Graph.
Example:
?- neighbours(4,[1-[3,5],2-[4],3-[], 4-[1,2,7,5],5-[],6-[],7-[],8-[]], NL). NL = [1,2,7,5]
- connect_ugraph(+UGraphIn, -Start, -UGraphOut) is det
- Adds Start as an additional vertex that is connected to all vertices
in UGraphIn. This can be used to create an topological sort for a
not connected graph. Start is before any vertex in UGraphIn in the
standard order of terms. No vertex in UGraphIn can be a variable.
Can be used to order a not-connected graph as follows:
top_sort_unconnected(Graph, Vertices) :- ( top_sort(Graph, Vertices) -> true ; connect_ugraph(Graph, Start, Connected), top_sort(Connected, Ordered0), Ordered0 = [Start|Vertices] ).
- complement(+UGraphIn, -UGraphOut)
- UGraphOut is a ugraph with an edge between all vertices that are
not connected in UGraphIn and all edges from UGraphIn removed.
Example:
?- complement([1-[3,5],2-[4],3-[], 4-[1,2,7,5],5-[],6-[],7-[],8-[]], NL). NL = [1-[2,4,6,7,8],2-[1,3,5,6,7,8],3-[1,2,4,5,6,7,8], 4-[3,5,6,8],5-[1,2,3,4,6,7,8],6-[1,2,3,4,5,7,8], 7-[1,2,3,4,5,6,8],8-[1,2,3,4,5,6,7]]
- reachable(+Vertex, +UGraph, -Vertices)
- True when Vertices is an ordered set of vertices reachable in
UGraph, including Vertex. Example:
?- reachable(1,[1-[3,5],2-[4],3-[],4-[5],5-[]],V). V = [1, 3, 5]
Re-exported predicates
The following predicates are exported from this file while their implementation is defined in imported modules or non-module files loaded by this module.
- ugraph_layers(Graph, -Layers) is semidet
- top_sort(+Graph, -Sorted) is semidet
- Sort vertices topologically. Layers is a list of lists of vertices
where there are no edges from a layer to an earlier layer. The
predicate top_sort/2 flattens the layers using append/2.
These predicates fail if Graph is cyclic. If Graph is not connected, the sub-graphs are individually sorted, where the root of each subgraph is in the first layer, the nodes connected to the roots in the second, etc.
?- top_sort([1-[2], 2-[3], 3-[]], L). L = [1, 2, 3]
- neighbors(+Vertex, +Graph, -Neigbours) is det
- neighbours(+Vertex, +Graph, -Neigbours) is det
- Neigbours is a sorted list of the neighbours of Vertex in Graph.
Example:
?- neighbours(4,[1-[3,5],2-[4],3-[], 4-[1,2,7,5],5-[],6-[],7-[],8-[]], NL). NL = [1,2,7,5]