- Documentation
- Reference manual
- The SWI-Prolog library
- library(aggregate): Aggregation operators on backtrackable predicates
- library(ansi_term): Print decorated text to ANSI consoles
- library(apply): Apply predicates on a list
- library(assoc): Association lists
- library(broadcast): Broadcast and receive event notifications
- library(charsio): I/O on Lists of Character Codes
- library(check): Consistency checking
- library(clpb): CLP(B): Constraint Logic Programming over Boolean Variables
- library(clpfd): CLP(FD): Constraint Logic Programming over Finite Domains
- library(clpqr): Constraint Logic Programming over Rationals and Reals
- library(csv): Process CSV (Comma-Separated Values) data
- library(dcg/basics): Various general DCG utilities
- library(dcg/high_order): High order grammar operations
- library(debug): Print debug messages and test assertions
- library(dicts): Dict utilities
- library(error): Error generating support
- library(fastrw): Fast reading and writing of terms
- library(gensym): Generate unique symbols
- library(heaps): heaps/priority queues
- library(increval): Incremental dynamic predicate modification
- library(intercept): Intercept and signal interface
- library(iostream): Utilities to deal with streams
- library(listing): List programs and pretty print clauses
- library(lists): List Manipulation
- library(macros): Macro expansion
- library(main): Provide entry point for scripts
- library(nb_set): Non-backtrackable set
- library(www_browser): Open a URL in the users browser
- library(occurs): Finding and counting sub-terms
- library(option): Option list processing
- library(optparse): command line parsing
- library(ordsets): Ordered set manipulation
- library(pairs): Operations on key-value lists
- library(persistency): Provide persistent dynamic predicates
- library(pio): Pure I/O
- library(portray_text): Portray text
- library(predicate_options): Declare option-processing of predicates
- library(prolog_coverage): Coverage analysis tool
- library(prolog_debug): User level debugging tools
- library(prolog_jiti): Just In Time Indexing (JITI) utilities
- library(prolog_trace): Print access to predicates
- library(prolog_versions): Demand specific (Prolog) versions
- library(prolog_xref): Prolog cross-referencer data collection
- library(quasi_quotations): Define Quasi Quotation syntax
- library(random): Random numbers
- library(rbtrees): Red black trees
- library(readutil): Read utilities
- library(record): Access named fields in a term
- library(registry): Manipulating the Windows registry
- library(rwlocks): Read/write locks
- library(settings): Setting management
- library(statistics): Get information about resource usage
- library(strings): String utilities
- library(simplex): Solve linear programming problems
- library(solution_sequences): Modify solution sequences
- library(tables): XSB interface to tables
- library(terms): Term manipulation
- library(thread): High level thread primitives
- library(thread_pool): Resource bounded thread management
- library(ugraphs): Graph manipulation library
- library(url): Analysing and constructing URL
- library(varnumbers): Utilities for numbered terms
- library(yall): Lambda expressions
- The SWI-Prolog library
- Packages
- Reference manual
A.60 library(ugraphs): Graph manipulation library
- author
- - R.A.O'Keefe
- Vitor Santos Costa
- Jan Wielemaker - license
- BSD-2 or Artistic 2.0
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]
- [det]vertices_edges_to_ugraph(+Vertices, +Edges, -UGraph)
- 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-[]]
- [det]del_vertices(+Graph, +Vertices, -NewGraph)
- 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-[]]- Compatibility
- Upto 5.6.48 the argument order was (+Vertices, +Graph, -NewGraph). Both YAP and SWI-Prolog have changed the argument order for compatibility with recent SICStus as well as consistency with del_edges/3.
- 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]]
- [det]transpose_ugraph(Graph, NewGraph)
- 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-[]]- Compatibility
- This predicate used to be known as transpose/2. Following SICStus 4, we reserve transpose/2 for matrix transposition and renamed ugraph transposition to transpose_ugraph/2.
- 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-[]]
- [semidet]ugraph_layers(Graph, -Layers)
- [semidet]top_sort(+Graph, -Sorted)
- 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]
- Compatibility
- - The original version of this library provided top_sort/3
as a difference list version of top_sort/2.
We removed this because the argument order was non-standard. Fixing
causes hard to debug compatibility issues while we expect top_sort/3
was rarely used. A backward compatible top_sort/3
can be defined as
top_sort(Graph, Tail, Sorted) :- top_sort(Graph, Sorted0), append(Sorted0, Tail, Sorted).The original version returned all vertices in a layer in reverse order. The current one returns them in standard order of terms, i.e., each layer is an ordered set.
- ugraph_layers/2 is a SWI-Prolog specific addition to this library.
- [det]neighbors(+Vertex, +Graph, -Neigbours)
- [det]neighbours(+Vertex, +Graph, -Neigbours)
- 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] - [det]connect_ugraph(+UGraphIn, -Start, -UGraphOut)
- 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]]- To be done
- Simple two-step algorithm. You could be smarter, I suppose.
- 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]