Module: RGL::MutableGraph
 Includes:
 Graph
 Included in:
 DirectedAdjacencyGraph
 Defined in:
 lib/rgl/mutable.rb,
lib/rgl/graphxml.rb
Overview
A MutableGraph can be changed via the addition or removal of edges and vertices.
Defined Under Namespace
Classes: MutableGraphParser
Instance Method Summary collapse

#acyclic? ⇒ Boolean
included
from Graph
Returns true if the graph contains no cycles.

#add_edge(u, v) ⇒ Object
Inserts the edge (u,v) into the graph.

#add_edges(*edges) ⇒ Object
Add all edges in the edges array to the edge set.

#add_vertex(v) ⇒ Object
Add a new vertex v to the graph.

#add_vertices(*a) ⇒ Object
Add all objects in a to the vertex set.

#adjacent_vertices(v) ⇒ Array
included
from Graph
Of vertices adjacent to vertex
v
. 
#bellman_ford_shortest_paths(edge_weights_map, source, visitor = BellmanFordVisitor.new(self)) ⇒ Hash[Object,Array]
included
from Graph
Finds the shortest paths from the source to each vertex of the graph.

#bfs_iterator(v = self.detect { x true }) ⇒ BFSIterator
included
from Graph
Starting at vertex v.

#bfs_search_tree_from(v) ⇒ DirectedAdjacencyGraph
included
from Graph
This method uses the
tree_edge_event
of BFSIterator to record all tree edges of the search tree in the result. 
#bipartite? ⇒ Boolean
included
from Graph
Returns true if the graph is bipartite.

#bipartite_sets ⇒ Array
included
from Graph
Separates graph’s vertices into two disjoint sets so that every edge of the graph connects vertices from different sets.

#condensation_graph ⇒ Object
included
from Graph
Returns an ImplicitGraph where the strongly connected components of this graph are condensed into single nodes represented by Set instances containing the members of each strongly connected component.

#cycles ⇒ Array
This is not an efficient implementation O(n^4) and could be done using Minimum Spanning Trees.

#cycles_with_vertex(vertex) ⇒ Array[Array]
Returns all minimum cycles that pass through a give vertex.

#depth_first_search(vis = DFSVisitor.new(self), &b) ⇒ Object
included
from Graph
Do a recursive DFS search on the whole graph.

#depth_first_visit(u, vis = DFSVisitor.new(self), &b) ⇒ Object
included
from Graph
Start a depth first search at vertex u.

#dfs_iterator(v = self.detect { x true }) ⇒ DFSIterator
included
from Graph
Staring at vertex v.

#dijkstra_shortest_path(edge_weights_map, source, target, visitor = DijkstraVisitor.new(self)) ⇒ Object
included
from Graph
Finds the shortest path from the source to the target in the graph.

#dijkstra_shortest_paths(edge_weights_map, source, visitor = DijkstraVisitor.new(self)) ⇒ Object
included
from Graph
Finds the shortest paths from the source to each vertex of the graph.

#directed? ⇒ Boolean
included
from Graph
Is the graph directed? The default returns false.

#dotty(params = {}) ⇒ Object
included
from Graph
Call dotty for the graph which is written to the file ‘graph.dot’ in the current directory.

#each(&block) ⇒ Object
included
from Graph
Vertices get enumerated.

#each_adjacent(v, &block) ⇒ Object
included
from Graph
The
each_adjacent
iterator defines the out edges of vertexv
. 
#each_connected_component {comp ... } ⇒ Object
included
from Graph
Compute the connected components of an undirected graph, using a DFS (Depthfirst search)based approach.

#each_edge(&block) ⇒ Object
included
from Graph
The
each_edge
iterator should provide efficient access to all edges of the graph. 
#each_vertex(&block) ⇒ Object
included
from Graph
The
each_vertex
iterator defines the set of vertices of the graph. 
#edge_class ⇒ Class
included
from Graph
The class for edges: Edge::DirectedEdge or Edge::UnDirectedEdge.

#edges ⇒ Array
included
from Graph
It uses Graph#each_edge to compute the edges.

#edges_filtered_by(&filter) ⇒ ImplicitGraph
included
from Graph
Returns a new ImplicitGraph which has as edges all edges of the receiver which satisfy the predicate filter (a block with two parameters).

#empty? ⇒ Boolean
included
from Graph
Returns true if the graph has no vertices, i.e.

#eql?(other) ⇒ Boolean
(also: #==)
included
from Graph
Two graphs are equal iff they have equal directed? property as well as vertices and edges sets.

#from_graphxml(source) ⇒ Object
Initializes an RGL graph from a subset of the GraphML format given in
source
(see graphml.graphdrawing.org/). 
#has_edge?(u, v) ⇒ Boolean
included
from Graph
Returns true if (u, v) is an edge of the graph.

#has_vertex?(v) ⇒ Boolean
included
from Graph
Returns true if
v
is a vertex of the graph. 
#implicit_graph {result ... } ⇒ ImplicitGraph
included
from Graph
Return a new ImplicitGraph which is isomorphic (i.e. has same edges and vertices) to the receiver.

#maximum_flow(edge_capacities_map, source, sink) ⇒ Hash
included
from Graph
Finds the maximum flow from the source to the sink in the graph.

#num_edges ⇒ int
included
from Graph
The number of edges.

#out_degree(v) ⇒ int
included
from Graph
Returns the number of outedges (for directed graphs) or the number of incident edges (for undirected graphs) of vertex
v
. 
#path?(source, target) ⇒ Boolean
included
from Graph
Checks whether a path exists between source and target vertices in the graph.

#prim_minimum_spanning_tree(edge_weights_map, start_vertex = nil, visitor = DijkstraVisitor.new(self)) ⇒ Object
included
from Graph
Finds the minimum spanning tree of the graph.

#print_dotted_on(params = {}, s = $stdout) ⇒ Object
included
from Graph
Output the DOTgraph to stream s.

#remove_edge(u, v) ⇒ Object
Remove the edge (u,v) from the graph.

#remove_vertex(v) ⇒ Object
Remove u from the vertex set of the graph.

#remove_vertices(*a) ⇒ Object
Remove all vertices specified by the array a from the graph by calling #remove_vertex.

#reverse ⇒ DirectedAdjacencyGraph
included
from Graph
Return a new DirectedAdjacencyGraph which has the same set of vertices.

#set_edge_options(u, v, **options) ⇒ Object
included
from Graph
Set the configuration values for the given edge.

#set_vertex_options(vertex, **options) ⇒ Object
included
from Graph
Set the configuration values for the given vertex.

#size ⇒ int
(also: #num_vertices)
included
from Graph
The number of vertices.

#strongly_connected_components ⇒ TarjanSccVisitor
included
from Graph
This is Tarjan’s algorithm for strongly connected components, from his paper “Depth first search and linear graph algorithms”.

#to_adjacency ⇒ DirectedAdjacencyGraph
included
from Graph
Convert a general graph to an AdjacencyGraph.

#to_dot_graph(params = {}) ⇒ Object
included
from Graph
Return a DOT::Digraph for directed graphs or a DOT::Graph for an undirected Graph.

#to_s ⇒ String
included
from Graph
Utility method to show a string representation of the edges of the graph.

#to_undirected ⇒ AdjacencyGraph
included
from Graph
Return a new AdjacencyGraph which has the same set of vertices.

#topsort_iterator ⇒ TopsortIterator
included
from Graph
For the graph.

#transitive_closure ⇒ Object
included
from Graph
Returns an DirectedAdjacencyGraph which is the transitive closure of this graph.

#transitive_reduction ⇒ Object
included
from Graph
Returns an DirectedAdjacencyGraph which is the transitive reduction of this graph.
 #vertex_id(v) ⇒ Object included from Graph

#vertex_label(v) ⇒ Object
included
from Graph
Returns a label for vertex v.

#vertices ⇒ Array
included
from Graph
Synonym for #to_a inherited by Enumerable.

#vertices_filtered_by(&filter) ⇒ ImplicitGraph
included
from Graph
Returns a new ImplicitGraph which has as vertices all vertices of the receiver which satisfy the predicate filter.

#write_to_graphic_file(fmt = 'png', dotfile = "graph", options = {}) ⇒ Object
included
from Graph
Use dot to create a graphical representation of the graph.
Instance Method Details
#acyclic? ⇒ Boolean Originally defined in module Graph
Returns true if the graph contains no cycles. This is only meaningful for directed graphs. Returns false for undirected graphs.
#add_edge(u, v) ⇒ Object
Inserts the edge (u,v) into the graph.
Note that for undirected graphs, (u,v) is the same edge as (v,u), so after a call to the function #add_edge, this implies that edge (u,v) will appear in the outedges of u and (u,v) (or equivalently (v,u)) will appear in the outedges of v. Put another way, v will be adjacent to u and u will be adjacent to v.
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# File 'lib/rgl/mutable.rb', line 29 def add_edge(u, v) raise NotImplementedError end 
#add_edges(*edges) ⇒ Object
Add all edges in the edges array to the edge set. Elements of the array can be both twoelement arrays or instances of Edge::DirectedEdge or Edge::UnDirectedEdge.
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# File 'lib/rgl/mutable.rb', line 43 def add_edges(*edges) edges.each { edge add_edge(edge[0], edge[1]) } end 
#add_vertex(v) ⇒ Object
Add a new vertex v to the graph. If the vertex is already in the graph (tested via eql?), the method does nothing.
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# File 'lib/rgl/mutable.rb', line 17 def add_vertex(v) raise NotImplementedError end 
#add_vertices(*a) ⇒ Object
Add all objects in a to the vertex set.
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# File 'lib/rgl/mutable.rb', line 35 def add_vertices(*a) a.each { v add_vertex v } end 
#adjacent_vertices(v) ⇒ Array Originally defined in module Graph
Returns of vertices adjacent to vertex v
.
#bellman_ford_shortest_paths(edge_weights_map, source, visitor = BellmanFordVisitor.new(self)) ⇒ Hash[Object,Array] Originally defined in module Graph
Finds the shortest paths from the source to each vertex of the graph.
Returns a Hash that maps each vertex of the graph to an Array of vertices that represents the shortest path from the source to the vertex. If the path doesn’t exist, the corresponding hash value is nil. For the source vertex returned hash contains a trivial onevertex path  [source].
Unlike Dijkstra algorithm, BellmanFord shortest paths algorithm works with negative edge weights.
Raises ArgumentError if an edge weight is undefined.
Raises ArgumentError or the graph has negativeweight cycles. This behavior can be overridden my a custom handler for visitor’s edge_not_minimized event.
#bfs_iterator(v = self.detect { x true }) ⇒ BFSIterator Originally defined in module Graph
Returns starting at vertex v.
#bfs_search_tree_from(v) ⇒ DirectedAdjacencyGraph Originally defined in module Graph
This method uses the tree_edge_event
of BFSIterator to record all tree edges of the search tree in the result.
#bipartite? ⇒ Boolean Originally defined in module Graph
Returns true if the graph is bipartite. Otherwise returns false.
#bipartite_sets ⇒ Array Originally defined in module Graph
Separates graph’s vertices into two disjoint sets so that every edge of the graph connects vertices from different sets. If it’s possible, the graph is bipartite.
Returns an array of two disjoint vertices sets (represented as arrays) if the graph is bipartite. Otherwise, returns nil.
#condensation_graph ⇒ Object Originally defined in module Graph
Returns an ImplicitGraph where the strongly connected components of this graph are condensed into single nodes represented by Set instances containing the members of each strongly connected component. Edges between the different strongly connected components are preserved while edges within strongly connected components are omitted.
Raises NotDirectedError if run on an undirected graph.
#cycles ⇒ Array
This is not an efficient implementation O(n^4) and could be done using Minimum Spanning Trees. Hint. Hint.
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# File 'lib/rgl/mutable.rb', line 99 def cycles g = self.clone self.inject([]) do acc, v acc = acc.concat(g.cycles_with_vertex(v)) g.remove_vertex(v); acc end end 
#cycles_with_vertex(vertex) ⇒ Array[Array]
Returns all minimum cycles that pass through a give vertex. The format is an Array of cycles, with each cycle being an Array of vertices in the cycle.
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# File 'lib/rgl/mutable.rb', line 78 def cycles_with_vertex(vertex) cycles_with_vertex_helper(vertex, vertex, []) end 
#depth_first_search(vis = DFSVisitor.new(self), &b) ⇒ Object Originally defined in module Graph
Do a recursive DFS search on the whole graph. If a block is passed, it is called on each finish_vertex
event. See #strongly_connected_components for an example usage.
Note that this traversal does not garantee, that roots are at the top of each spanning subtree induced by the DFS search on a directed graph (see also the discussion in issue #20).
#depth_first_visit(u, vis = DFSVisitor.new(self), &b) ⇒ Object Originally defined in module Graph
Start a depth first search at vertex u. The block b is called on each finish_vertex
event.
#dfs_iterator(v = self.detect { x true }) ⇒ DFSIterator Originally defined in module Graph
Returns staring at vertex v.
#dijkstra_shortest_path(edge_weights_map, source, target, visitor = DijkstraVisitor.new(self)) ⇒ Object Originally defined in module Graph
Finds the shortest path from the source to the target in the graph.
If the path exists, returns it as an Array of vertices. Otherwise, returns nil.
Raises ArgumentError if edge weight is negative or undefined.
#dijkstra_shortest_paths(edge_weights_map, source, visitor = DijkstraVisitor.new(self)) ⇒ Object Originally defined in module Graph
Finds the shortest paths from the source to each vertex of the graph.
Returns a Hash that maps each vertex of the graph to an Array of vertices that represents the shortest path from the source to the vertex. If the path doesn’t exist, the corresponding hash value is nil. For the source vertex returned hash contains a trivial onevertex path  [source].
Raises ArgumentError if edge weight is negative or undefined.
#directed? ⇒ Boolean Originally defined in module Graph
Is the graph directed? The default returns false.
#dotty(params = {}) ⇒ Object Originally defined in module Graph
Call dotty for the graph which is written to the file ‘graph.dot’ in the current directory.
#each(&block) ⇒ Object Originally defined in module Graph
Vertices get enumerated. A graph is thus an enumerable of vertices.
#each_adjacent(v, &block) ⇒ Object Originally defined in module Graph
The each_adjacent
iterator defines the out edges of vertex v
. This method must be defined by concrete graph classes. Its defines the BGL IncidenceGraph concept.
#each_connected_component {comp ... } ⇒ Object Originally defined in module Graph
Compute the connected components of an undirected graph, using a DFS (Depthfirst search)based approach. A _connected component_ of an undirected graph is a set of vertices that are all reachable from each other.
The function is implemented as an iterator which calls the client with an array of vertices for each component.
It raises an exception if the graph is directed.
#each_edge(&block) ⇒ Object Originally defined in module Graph
The each_edge
iterator should provide efficient access to all edges of the graph. Its defines the BGL EdgeListGraph concept.
This method must not be defined by concrete graph classes, because it can be implemented using #each_vertex and #each_adjacent. However for undirected graphs the function is inefficient because we must not yield (v,u) if we already visited edge (u,v).
#each_vertex(&block) ⇒ Object Originally defined in module Graph
The each_vertex
iterator defines the set of vertices of the graph. This method must be defined by concrete graph classes. It defines the BGL VertexListGraph concept.
#edge_class ⇒ Class Originally defined in module Graph
Returns the class for edges: Edge::DirectedEdge or Edge::UnDirectedEdge.
#edges ⇒ Array Originally defined in module Graph
It uses #each_edge to compute the edges
#edges_filtered_by(&filter) ⇒ ImplicitGraph Originally defined in module Graph
Returns a new ImplicitGraph which has as edges all edges of the receiver which satisfy the predicate filter (a block with two parameters).
#empty? ⇒ Boolean Originally defined in module Graph
Returns true if the graph has no vertices, i.e. num_vertices == 0.
#eql?(other) ⇒ Boolean Also known as: == Originally defined in module Graph
Two graphs are equal iff they have equal directed? property as well as vertices and edges sets.
#from_graphxml(source) ⇒ Object
Initializes an RGL graph from a subset of the GraphML format given in source
(see graphml.graphdrawing.org/).
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# File 'lib/rgl/graphxml.rb', line 53 def from_graphxml(source) listener = MutableGraphParser.new(self) REXML::Document.parse_stream(source, listener) self end 
#has_edge?(u, v) ⇒ Boolean Originally defined in module Graph
Returns true if (u, v) is an edge of the graph.
#has_vertex?(v) ⇒ Boolean Originally defined in module Graph
Returns true if v
is a vertex of the graph. Same as #include? inherited from Enumerable. Complexity is O(num_vertices) by default. Concrete graph may be better here (see AdjacencyGraph).
#implicit_graph {result ... } ⇒ ImplicitGraph Originally defined in module Graph
Return a new ImplicitGraph which is isomorphic (i.e. has same edges and vertices) to the receiver. It is a shortcut, also used by #edges_filtered_by and #vertices_filtered_by.
#maximum_flow(edge_capacities_map, source, sink) ⇒ Hash Originally defined in module Graph
Finds the maximum flow from the source to the sink in the graph.
Returns flows map as a hash that maps each edge of the graph to a flow through that edge that is required to reach the maximum total flow.
For the method to work, the graph should be first altered so that for each directed edge (u, v) it contains reverse edge (u, v). Capacities of the primary edges should be nonnegative, while reverse edges should have zero capacity.
Raises ArgumentError if the graph is not directed.
Raises ArgumentError if a reverse edge is missing, edge capacity is missing, an edge has negative capacity, or a reverse edge has positive capacity.
#num_edges ⇒ int Originally defined in module Graph
Returns the number of edges.
#out_degree(v) ⇒ int Originally defined in module Graph
Returns the number of outedges (for directed graphs) or the number of incident edges (for undirected graphs) of vertex v
.
#path?(source, target) ⇒ Boolean Originally defined in module Graph
Checks whether a path exists between source and target vertices in the graph.
#prim_minimum_spanning_tree(edge_weights_map, start_vertex = nil, visitor = DijkstraVisitor.new(self)) ⇒ Object Originally defined in module Graph
Finds the minimum spanning tree of the graph.
Returns an AdjacencyGraph that represents the minimum spanning tree of the graph’s connectivity component that contains the starting vertex. The algorithm starts from an arbitrary vertex if the start_vertex is not given. Since the implementation relies on the Dijkstra’s algorithm, Prim’s algorithm uses the same visitor class and emits the same events.
Raises ArgumentError if edge weight is undefined.
#print_dotted_on(params = {}, s = $stdout) ⇒ Object Originally defined in module Graph
Output the DOTgraph to stream s.
#remove_edge(u, v) ⇒ Object
Remove the edge (u,v) from the graph. If the graph allows parallel edges, this removes all occurrences of (u,v).
Precondition: u and v are vertices in the graph. Postcondition: (u,v) is no longer in the edge set for g.
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# File 'lib/rgl/mutable.rb', line 63 def remove_edge(u, v) raise NotImplementedError end 
#remove_vertex(v) ⇒ Object
Remove u from the vertex set of the graph. All edges whose target is v are also removed from the edge set of the graph.
Postcondition: num_vertices is one less, v no longer appears in the vertex set of the graph, and there no edge with source or target v.
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# File 'lib/rgl/mutable.rb', line 53 def remove_vertex(v) raise NotImplementedError end 
#remove_vertices(*a) ⇒ Object
Remove all vertices specified by the array a from the graph by calling #remove_vertex.
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# File 'lib/rgl/mutable.rb', line 70 def remove_vertices(*a) a.each { v remove_vertex v } end 
#reverse ⇒ DirectedAdjacencyGraph Originally defined in module Graph
Return a new DirectedAdjacencyGraph which has the same set of vertices. If (u,v) is an edge of the graph, then (v,u) is an edge of the result.
If the graph is undirected, the result is self.
#set_edge_options(u, v, **options) ⇒ Object Originally defined in module Graph
Set the configuration values for the given edge
#set_vertex_options(vertex, **options) ⇒ Object Originally defined in module Graph
Set the configuration values for the given vertex
#size ⇒ int Also known as: num_vertices Originally defined in module Graph
Returns the number of vertices.
#strongly_connected_components ⇒ TarjanSccVisitor Originally defined in module Graph
This is Tarjan’s algorithm for strongly connected components, from his paper “Depth first search and linear graph algorithms”. It calculates the components in a single application of DFS. We implement the algorithm with the help of the DFSVisitor TarjanSccVisitor.
Definition
A _strongly connected component_ of a directed graph G=(V,E) is a maximal set of vertices U which is in V, such that for every pair of vertices u and v in U, we have both a path from u to v and a path from v to u. That is to say, u and v are reachable from each other.
@Article{Tarjan:1972:DFS,
author = "R. E. Tarjan",
key = "Tarjan",
title = "Depth First Search and Linear Graph Algorithms",
journal = "SIAM Journal on Computing",
volume = "1",
number = "2",
pages = "146160",
month = jun,
year = "1972",
CODEN = "SMJCAT",
ISSN = "00975397 (print), 10957111 (electronic)",
bibdate = "Thu Jan 23 09:56:44 1997",
bibsource = "Parallel/Multi.bib, Misc/Reverse.eng.bib",
}
The output of the algorithm is recorded in a TarjanSccVisitor vis. vis.comp_map
will contain numbers giving the component ID assigned to each vertex. The number of components is vis.num_comp
.
#to_adjacency ⇒ DirectedAdjacencyGraph Originally defined in module Graph
Convert a general graph to an AdjacencyGraph. If the graph is directed, returns a DirectedAdjacencyGraph; otherwise, returns an AdjacencyGraph.
#to_dot_graph(params = {}) ⇒ Object Originally defined in module Graph
Return a DOT::Digraph for directed graphs or a DOT::Graph for an undirected RGL::Graph. params can contain any graph property specified in rdot.rb.
#to_s ⇒ String Originally defined in module Graph
Utility method to show a string representation of the edges of the graph.
#to_undirected ⇒ AdjacencyGraph Originally defined in module Graph
Return a new AdjacencyGraph which has the same set of vertices. If (u,v) is an edge of the graph, then (u,v) and (v,u) (which are the same edges) are edges of the result.
If the graph is undirected, the result is self
.
#topsort_iterator ⇒ TopsortIterator Originally defined in module Graph
Returns for the graph.
#transitive_closure ⇒ Object Originally defined in module Graph
Returns an DirectedAdjacencyGraph which is the transitive closure of this graph. Meaning, for each path u > … > v in this graph, the path is copied and the edge u > v is added. This method supports working with cyclic graphs by ensuring that edges are created between every pair of vertices in the cycle, including selfreferencing edges.
This method should run in O(VE) time, where V and E are the number of vertices and edges respectively.
Raises NotDirectedError if run on an undirected graph.
#transitive_reduction ⇒ Object Originally defined in module Graph
Returns an DirectedAdjacencyGraph which is the transitive reduction of this graph. Meaning, that each edge u > v is omitted if path u > … > v exists. This method supports working with cyclic graphs; however, cycles are arbitrarily simplified which may lead to variant, although equally valid, results on equivalent graphs.
This method should run in O(VE) time, where V and E are the number of vertices and edges respectively.
Raises NotDirectedError if run on an undirected graph.
#vertex_id(v) ⇒ Object Originally defined in module Graph
#vertex_label(v) ⇒ Object Originally defined in module Graph
Returns a label for vertex v. Default is v.to_s
#vertices ⇒ Array Originally defined in module Graph
Synonym for #to_a inherited by Enumerable.
#vertices_filtered_by(&filter) ⇒ ImplicitGraph Originally defined in module Graph
Returns a new ImplicitGraph which has as vertices all vertices of the receiver which satisfy the predicate filter.
The methods provides similar functionality as BGLs Filtered Graph