Class: Bio::Pathway
Overview
Bio::Pathway is a general graph object initially constructed by the list of the ((<Bio::Relation>)) objects. The basic concept of the Bio::Pathway object is to store a graph as an adjacency list (in the instance variable @graph), and converting the list into an adjacency matrix by calling to_matrix method on demand. However, in some cases, it is convenient to have the original list of the ((<Bio::Relation>))s, Bio::Pathway object also stores the list (as the instance variable @relations) redundantly.
Note: you can clear the @relations list by calling clear_relations! method to reduce the memory usage, and the content of the @relations can be re-generated from the @graph by to_relations method.
Direct Known Subclasses
Instance Attribute Summary collapse
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#graph ⇒ Object
readonly
Read-only accessor for the adjacency list of the graph.
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#index ⇒ Object
readonly
Read-only accessor for the row/column index (@index) of the adjacency matrix.
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#label ⇒ Object
Accessor for the hash of the label assigned to the each node.
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#relations ⇒ Object
readonly
Read-only accessor for the internal list of the Bio::Relation objects.
Instance Method Summary collapse
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#append(rel, add_rel = true) ⇒ Object
Add an Bio::Relation object ‘rel’ to the @graph and @relations.
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#bellman_ford(root) ⇒ Object
Bellman-Ford method for solving the single-source shortest-paths problem in the graph in which edge weights can be negative.
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#bfs_shortest_path(node1, node2) ⇒ Object
Calculates the shortest path between two nodes by using breadth_first_search method and returns steps and the path as Array.
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#breadth_first_search(root) ⇒ Object
(also: #bfs)
Breadth first search solves steps and path to the each node and forms a tree contains all reachable vertices from the root node.
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#clear_relations! ⇒ Object
Clear @relations array to reduce the memory usage.
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#clique ⇒ Object
Not implemented yet.
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#cliquishness(node) ⇒ Object
Returns completeness of the edge density among the surrounded nodes.
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#common_subgraph(graph) ⇒ Object
Not implemented yet.
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#delete(rel) ⇒ Object
Remove an edge indicated by the Bio::Relation object ‘rel’ from the.
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#depth_first_search ⇒ Object
(also: #dfs)
Depth first search yields much information about the structure of the graph especially on the classification of the edges.
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#dfs_topological_sort ⇒ Object
Topological sort of the directed acyclic graphs (“dags”) by using depth_first_search.
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#dijkstra(root) ⇒ Object
Dijkstra method to solve the shortest path problem in the weighted graph.
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#directed ⇒ Object
Changes the internal state of the graph from ‘undirected’ to ‘directed’ and re-generate adjacency list.
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#directed? ⇒ Boolean
Returns true or false respond to the internal state of the graph.
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#dump_list ⇒ Object
Pretty printer of the adjacency list.
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#dump_matrix(*arg) ⇒ Object
Pretty printer of the adjacency matrix.
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#edges ⇒ Object
Returns the number of the edges in the graph.
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#floyd_warshall ⇒ Object
(also: #floyd)
Floyd-Wardshall alogrithm for solving the all-pairs shortest-paths problem on a directed graph G = (V, E).
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#initialize(relations, undirected = false) ⇒ Pathway
constructor
Initial graph (adjacency list) generation from the list of Relation.
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#kruskal ⇒ Object
Kruskal method for finding minimam spaninng trees.
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#nodes ⇒ Object
Returns the number of the nodes in the graph.
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#small_world ⇒ Object
Returns frequency of the nodes having same number of edges as hash.
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#subgraph(list = nil) ⇒ Object
Select labeled nodes and generate subgraph.
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#to_list ⇒ Object
Graph (adjacency list) generation from the Relations.
-
#to_matrix(default_value = nil, diagonal_value = nil) ⇒ Object
Convert adjacency list to adjacency matrix.
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#to_relations ⇒ Object
Reconstruct @relations from the adjacency list @graph.
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#undirected ⇒ Object
Changes the internal state of the graph from ‘directed’ to ‘undirected’ and re-generate adjacency list.
-
#undirected? ⇒ Boolean
Returns true or false respond to the internal state of the graph.
Constructor Details
#initialize(relations, undirected = false) ⇒ Pathway
Initial graph (adjacency list) generation from the list of Relation.
Generate Bio::Pathway object from the list of Bio::Relation objects. If the second argument is true, undirected graph is generated.
r1 = Bio::Relation.new('a', 'b', 1)
r2 = Bio::Relation.new('a', 'c', 5)
r3 = Bio::Relation.new('b', 'c', 3)
list = [ r1, r2, r3 ]
g = Bio::Pathway.new(list, 'undirected')
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# File 'lib/bio/pathway.rb', line 41 def initialize(relations, undirected = false) @undirected = undirected @relations = relations @graph = {} # adjacency list expression of the graph @index = {} # numbering each node in matrix @label = {} # additional information on each node self.to_list # generate adjacency list end |
Instance Attribute Details
#graph ⇒ Object (readonly)
Read-only accessor for the adjacency list of the graph.
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# File 'lib/bio/pathway.rb', line 54 def graph @graph end |
#index ⇒ Object (readonly)
Read-only accessor for the row/column index (@index) of the adjacency matrix. Contents of the hash @index is created by calling to_matrix method.
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# File 'lib/bio/pathway.rb', line 59 def index @index end |
#label ⇒ Object
Accessor for the hash of the label assigned to the each node. You can label some of the nodes in the graph by passing a hash to the label and select subgraphs which contain labeled nodes only by subgraph method.
hash = { 1 => 'red', 2 => 'green', 5 => 'black' }
g.label = hash
g.label
g.subgraph # => new graph consists of the node 1, 2, 5 only
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# File 'lib/bio/pathway.rb', line 70 def label @label end |
#relations ⇒ Object (readonly)
Read-only accessor for the internal list of the Bio::Relation objects
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# File 'lib/bio/pathway.rb', line 51 def relations @relations end |
Instance Method Details
#append(rel, add_rel = true) ⇒ Object
Add an Bio::Relation object ‘rel’ to the @graph and @relations. If the second argument is false, @relations is not modified (only useful when genarating @graph from @relations internally).
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# File 'lib/bio/pathway.rb', line 144 def append(rel, add_rel = true) @relations.push(rel) if add_rel if @graph[rel.from].nil? @graph[rel.from] = {} end if @graph[rel.to].nil? @graph[rel.to] = {} end @graph[rel.from][rel.to] = rel.relation @graph[rel.to][rel.from] = rel.relation if @undirected end |
#bellman_ford(root) ⇒ Object
Bellman-Ford method for solving the single-source shortest-paths problem in the graph in which edge weights can be negative.
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# File 'lib/bio/pathway.rb', line 486 def bellman_ford(root) distance, predecessor = initialize_single_source(root) for i in 1 ..(self.nodes - 1) do @graph.each_key do |u| @graph[u].each do |v, w| # relaxing procedure of root -> 'u' -> 'v' if distance[v] > distance[u] + w distance[v] = distance[u] + w predecessor[v] = u end end end end # negative cyclic loop check @graph.each_key do |u| @graph[u].each do |v, w| if distance[v] > distance[u] + w return false end end end return distance, predecessor end |
#bfs_shortest_path(node1, node2) ⇒ Object
Calculates the shortest path between two nodes by using breadth_first_search method and returns steps and the path as Array.
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# File 'lib/bio/pathway.rb', line 375 def bfs_shortest_path(node1, node2) distance, route = breadth_first_search(node1) step = distance[node2] node = node2 path = [ node2 ] while node != node1 and route[node] node = route[node] path.unshift(node) end return step, path end |
#breadth_first_search(root) ⇒ Object Also known as: bfs
Breadth first search solves steps and path to the each node and forms a tree contains all reachable vertices from the root node. This method returns the result in 2 hashes - 1st one shows the steps from root node and 2nd hash shows the structure of the tree.
The weight of the edges are not considered in this method.
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# File 'lib/bio/pathway.rb', line 344 def breadth_first_search(root) visited = {} distance = {} predecessor = {} visited[root] = true distance[root] = 0 predecessor[root] = nil queue = [ root ] while from = queue.shift next unless @graph[from] @graph[from].each_key do |to| unless visited[to] visited[to] = true distance[to] = distance[from] + 1 predecessor[to] = from queue.push(to) end end end return distance, predecessor end |
#clear_relations! ⇒ Object
Clear @relations array to reduce the memory usage.
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# File 'lib/bio/pathway.rb', line 114 def clear_relations! @relations.clear end |
#clique ⇒ Object
Not implemented yet.
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# File 'lib/bio/pathway.rb', line 304 def clique raise NotImplementedError end |
#cliquishness(node) ⇒ Object
Returns completeness of the edge density among the surrounded nodes.
Calculates the value of cliquishness around the ‘node’. This value indicates completeness of the edge density among the surrounded nodes.
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# File 'lib/bio/pathway.rb', line 313 def cliquishness(node) neighbors = @graph[node].keys sg = subgraph(neighbors) if sg.graph.size != 0 edges = sg.edges / 2.0 nodes = sg.nodes complete = (nodes * (nodes - 1)) / 2.0 return edges/complete else return 0.0 end end |
#common_subgraph(graph) ⇒ Object
Not implemented yet.
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# File 'lib/bio/pathway.rb', line 298 def common_subgraph(graph) raise NotImplementedError end |
#delete(rel) ⇒ Object
Remove an edge indicated by the Bio::Relation object ‘rel’ from the
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# File 'lib/bio/pathway.rb', line 158 def delete(rel) @relations.delete_if do |x| x === rel end @graph[rel.from].delete(rel.to) @graph[rel.to].delete(rel.from) if @undirected end |
#depth_first_search ⇒ Object Also known as: dfs
Depth first search yields much information about the structure of the graph especially on the classification of the edges. This method returns 5 hashes - 1st one shows the timestamps of each node containing the first discoverd time and the search finished time in an array. The 2nd, 3rd, 4th, and 5th hashes contain ‘tree edges’, ‘back edges’, ‘cross edges’, ‘forward edges’ respectively.
If $DEBUG is true (e.g. ruby -d), this method prints the progression of the search.
The weight of the edges are not considered in this method.
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# File 'lib/bio/pathway.rb', line 399 def depth_first_search visited = {} = {} tree_edges = {} back_edges = {} cross_edges = {} forward_edges = {} count = 0 dfs_visit = Proc.new { |from| visited[from] = true [from] = [count += 1] @graph[from].each_key do |to| if visited[to] if [to].size > 1 if [from].first < [to].first # forward edge (black) p "#{from} -> #{to} : forward edge" if $DEBUG forward_edges[from] = to else # cross edge (black) p "#{from} -> #{to} : cross edge" if $DEBUG cross_edges[from] = to end else # back edge (gray) p "#{from} -> #{to} : back edge" if $DEBUG back_edges[from] = to end else # tree edge (white) p "#{from} -> #{to} : tree edge" if $DEBUG tree_edges[to] = from dfs_visit.call(to) end end [from].push(count += 1) } @graph.each_key do |node| unless visited[node] dfs_visit.call(node) end end return , tree_edges, back_edges, cross_edges, forward_edges end |
#dfs_topological_sort ⇒ Object
Topological sort of the directed acyclic graphs (“dags”) by using depth_first_search.
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# File 'lib/bio/pathway.rb', line 452 def dfs_topological_sort # sorted by finished time reversely and collect node names only , = self.depth_first_search .sort {|a,b| b[1][1] <=> a[1][1]}.collect {|x| x.first } end |
#dijkstra(root) ⇒ Object
Dijkstra method to solve the shortest path problem in the weighted graph.
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# File 'lib/bio/pathway.rb', line 460 def dijkstra(root) distance, predecessor = initialize_single_source(root) @graph[root].each do |k, v| distance[k] = v predecessor[k] = root end queue = distance.dup queue.delete(root) while queue.size != 0 min = queue.min {|a, b| a[1] <=> b[1]} u = min[0] # extranct a node having minimal distance @graph[u].each do |k, v| # relaxing procedure of root -> 'u' -> 'k' if distance[k] > distance[u] + v distance[k] = distance[u] + v predecessor[k] = u end end queue.delete(u) end return distance, predecessor end |
#directed ⇒ Object
Changes the internal state of the graph from ‘undirected’ to ‘directed’ and re-generate adjacency list. The undirected graph can be converted to directed graph, however, the edge between two nodes will be simply doubled to both ends.
Note: this method can not be used without the list of the Bio::Relation objects (internally stored in @relations variable). Thus if you already called clear_relations! method, call to_relations first.
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# File 'lib/bio/pathway.rb', line 92 def directed if undirected? @undirected = false self.to_list end end |
#directed? ⇒ Boolean
Returns true or false respond to the internal state of the graph.
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# File 'lib/bio/pathway.rb', line 74 def directed? @undirected ? false : true end |
#dump_list ⇒ Object
Pretty printer of the adjacency list.
The dump_matrix method accepts the same arguments as to_matrix. Useful when you want to check the internal state of the adjacency list (for debug purpose etc.) easily.
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# File 'lib/bio/pathway.rb', line 251 def dump_list list = "" @graph.each do |from, hash| list << "#{from} => " a = [] hash.each do |to, relation| a.push("#{to} (#{relation})") end list << a.join(", ") + "\n" end list end |
#dump_matrix(*arg) ⇒ Object
Pretty printer of the adjacency matrix.
The dump_matrix method accepts the same arguments as to_matrix. Useful when you want to check the internal state of the matrix (for debug purpose etc.) easily.
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# File 'lib/bio/pathway.rb', line 239 def dump_matrix(*arg) matrix = self.to_matrix(*arg) sorted = @index.sort {|a,b| a[1] <=> b[1]} "[# " + sorted.collect{|x| x[0]}.join(", ") + "\n" + matrix.to_a.collect{|row| ' ' + row.inspect}.join(",\n") + "\n]" end |
#edges ⇒ Object
Returns the number of the edges in the graph.
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# File 'lib/bio/pathway.rb', line 172 def edges edges = 0 @graph.each_value do |v| edges += v.size end edges end |
#floyd_warshall ⇒ Object Also known as: floyd
Floyd-Wardshall alogrithm for solving the all-pairs shortest-paths problem on a directed graph G = (V, E).
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# File 'lib/bio/pathway.rb', line 513 def floyd_warshall inf = 1 / 0.0 m = self.to_matrix(inf, 0) d = m.dup n = self.nodes for k in 0 .. n - 1 do for i in 0 .. n - 1 do for j in 0 .. n - 1 do if d[i, j] > d[i, k] + d[k, j] d[i, j] = d[i, k] + d[k, j] end end end end return d end |
#kruskal ⇒ Object
Kruskal method for finding minimam spaninng trees
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# File 'lib/bio/pathway.rb', line 535 def kruskal # initialize rel = self.to_relations.sort{|a, b| a <=> b} index = [] for i in 0 .. (rel.size - 1) do for j in (i + 1) .. (rel.size - 1) do if rel[i] == rel[j] index << j end end end index.sort{|x, y| y<=>x}.each do |i| rel[i, 1] = [] end mst = [] seen = Hash.new() @graph.each_key do |x| seen[x] = nil end i = 1 # initialize end rel.each do |r| if seen[r.node[0]] == nil seen[r.node[0]] = 0 end if seen[r.node[1]] == nil seen[r.node[1]] = 0 end if seen[r.node[0]] == seen[r.node[1]] && seen[r.node[0]] == 0 mst << r seen[r.node[0]] = i seen[r.node[1]] = i elsif seen[r.node[0]] != seen[r.node[1]] mst << r v1 = seen[r.node[0]].dup v2 = seen[r.node[1]].dup seen.each do |k, v| if v == v1 || v == v2 seen[k] = i end end end i += 1 end return Pathway.new(mst) end |
#nodes ⇒ Object
Returns the number of the nodes in the graph.
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# File 'lib/bio/pathway.rb', line 167 def nodes @graph.keys.length end |
#small_world ⇒ Object
Returns frequency of the nodes having same number of edges as hash
Calculates the frequency of the nodes having the same number of edges and returns the value as Hash.
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# File 'lib/bio/pathway.rb', line 330 def small_world freq = Hash.new(0) @graph.each_value do |v| freq[v.size] += 1 end return freq end |
#subgraph(list = nil) ⇒ Object
Select labeled nodes and generate subgraph
This method select some nodes and returns new Bio::Pathway object consists of selected nodes only. If the list of the nodes (as Array) is assigned as the argument, use the list to select the nodes from the graph. If no argument is assigned, internal property of the graph @label is used to select the nodes.
hash = { 'a' => 'secret', 'b' => 'important', 'c' => 'important' }
g.label = hash
g.subgraph
list = [ 'a', 'b', 'c' ]
g.subgraph(list)
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# File 'lib/bio/pathway.rb', line 278 def subgraph(list = nil) if list @label.clear list.each do |node| @label[node] = true end end sub_graph = Pathway.new([], @undirected) @graph.each do |from, hash| next unless @label[from] hash.each do |to, relation| next unless @label[to] sub_graph.append(Relation.new(from, to, relation)) end end return sub_graph end |
#to_list ⇒ Object
Graph (adjacency list) generation from the Relations
Generate the adjcancecy list @graph from @relations (called by initialize and in some other cases when @relations has been changed).
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# File 'lib/bio/pathway.rb', line 134 def to_list @graph.clear @relations.each do |rel| append(rel, false) # append to @graph without push to @relations end end |
#to_matrix(default_value = nil, diagonal_value = nil) ⇒ Object
Convert adjacency list to adjacency matrix
Returns the adjacency matrix expression of the graph as a Matrix object. If the first argument was assigned, the matrix will be filled with the given value. The second argument indicates the value of the diagonal constituents of the matrix besides the above.
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# File 'lib/bio/pathway.rb', line 187 def to_matrix(default_value = nil, diagonal_value = nil) #-- # Note: following code only fills the outer Array with the reference # to the same inner Array object. # # matrix = Array.new(nodes, Array.new(nodes)) # # so create a new Array object for each row as follows: #++ matrix = Array.new nodes.times do matrix.push(Array.new(nodes, default_value)) end if diagonal_value nodes.times do |i| matrix[i][i] = diagonal_value end end # assign index number for each node @graph.keys.each_with_index do |k, i| @index[k] = i end if @relations.empty? # only used after clear_relations! @graph.each do |from, hash| hash.each do |to, relation| x = @index[from] y = @index[to] matrix[x][y] = relation end end else @relations.each do |rel| x = @index[rel.from] y = @index[rel.to] matrix[x][y] = rel.relation matrix[y][x] = rel.relation if @undirected end end Matrix[*matrix] end |
#to_relations ⇒ Object
Reconstruct @relations from the adjacency list @graph.
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# File 'lib/bio/pathway.rb', line 119 def to_relations @relations.clear @graph.each_key do |from| @graph[from].each do |to, w| @relations << Relation.new(from, to, w) end end return @relations end |
#undirected ⇒ Object
Changes the internal state of the graph from ‘directed’ to ‘undirected’ and re-generate adjacency list.
Note: this method can not be used without the list of the Bio::Relation objects (internally stored in @relations variable). Thus if you already called clear_relations! method, call to_relations first.
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# File 'lib/bio/pathway.rb', line 106 def undirected if directed? @undirected = true self.to_list end end |
#undirected? ⇒ Boolean
Returns true or false respond to the internal state of the graph.
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# File 'lib/bio/pathway.rb', line 79 def undirected? @undirected ? true : false end |