class Bio::Pathway

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.

Attributes

graph[R]

Read-only accessor for the adjacency list of the graph.

index[R]

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.

label[RW]

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
relations[R]

Read-only accessor for the internal list of the Bio::Relation objects

Public Class Methods

new(relations, undirected = false) click to toggle source

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')
# 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

Public Instance Methods

append(rel, add_rel = true) click to toggle source

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).

# 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) click to toggle source

Bellman-Ford method for solving the single-source shortest-paths problem in the graph in which edge weights can be negative.

# File lib/bio/pathway.rb, line 592
def bellman_ford(root)
  distance, predecessor = initialize_single_source(root)
  (self.nodes - 1).times 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(root)

Alias for the #breadth_first_search method.

bfs_shortest_path(node1, node2) click to toggle source

Calculates the shortest path between two nodes by using #breadth_first_search method and returns steps and the path as Array.

# File lib/bio/pathway.rb, line 450
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
clear_relations!() click to toggle source

Clear @relations array to reduce the memory usage.

# File lib/bio/pathway.rb, line 114
def clear_relations!
  @relations.clear
end
clique() click to toggle source

Not implemented yet.

# File lib/bio/pathway.rb, line 370
def clique
  raise NotImplementedError
end
cliquishness(node) click to toggle source

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.

Note: cliquishness (clustering coefficient) for a directed graph is also calculated. Reference: en.wikipedia.org/wiki/Clustering_coefficient

Note: Cliquishness (clustering coefficient) for a node that has only one neighbor node is undefined. Currently, it returns NaN, but the behavior may be changed in the future.

# File lib/bio/pathway.rb, line 388
def cliquishness(node)
  neighbors = @graph[node].keys
  sg = subgraph(neighbors)
  if sg.graph.size != 0
    edges = sg.edges
    nodes = neighbors.size
    complete = (nodes * (nodes - 1))
    return edges.quo(complete)
  else
    return 0.0
  end
end
common_subgraph(graph) click to toggle source

Not implemented yet.

# File lib/bio/pathway.rb, line 364
def common_subgraph(graph)
  raise NotImplementedError
end
delete(rel) click to toggle source

Remove an edge indicated by the Bio::Relation object 'rel' from the @graph and the @relations.

# 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
dfs()

Alias for the #depth_first_search method.

Alias for: depth_first_search
dfs_topological_sort() click to toggle source

Topological sort of the directed acyclic graphs (“dags”) by using depth_first_search.

# File lib/bio/pathway.rb, line 558
def dfs_topological_sort
  # sorted by finished time reversely and collect node names only
  timestamp, = self.depth_first_search
  timestamp.sort {|a,b| b[1][1] <=> a[1][1]}.collect {|x| x.first }
end
dijkstra(root) click to toggle source

Dijkstra method to solve the shortest path problem in the weighted graph.

# File lib/bio/pathway.rb, line 566
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() click to toggle source

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.

# File lib/bio/pathway.rb, line 92
def directed
  if undirected?
    @undirected = false
    self.to_list
  end
end
directed?() click to toggle source

Returns true or false respond to the internal state of the graph.

# File lib/bio/pathway.rb, line 74
def directed?
  @undirected ? false : true
end
dump_list() click to toggle source

Pretty printer of the adjacency list.

Useful when you want to check the internal state of the adjacency list (for debug purpose etc.) easily.

The result of this method depends on the order of Hash#each (and each_key, etc.), which may be variable with Ruby version and Ruby interpreter variations (JRuby, etc.). For a workaround to remove such dependency, you can use @index to set order of Hash keys. Note that this behavior might be changed in the future.

# File lib/bio/pathway.rb, line 293
def dump_list
  # begin workaround removing depencency to order of Hash#each
  if @index.empty? then
    pref = nil
    enum = @graph
  else
    pref = {}.merge(@index)
    i = pref.values.max
    @graph.each_key do |node|
      pref[node] ||= (i += 1)
    end
    graph_to_a = @graph.to_a
    graph_to_a.sort! { |x, y| pref[x[0]] <=> pref[y[0]] }
    enum = graph_to_a
  end
  # end workaround removing depencency to order of Hash#each

  list = ""
  enum.each do |from, hash|
    list << "#{from} => "
    # begin workaround removing depencency to order of Hash#each
    if pref then
      ary = hash.to_a
      ary.sort! { |x,y| pref[x[0]] <=> pref[y[0]] }
      hash = ary
    end
    # end workaround removing depencency to order of Hash#each
    a = []
    hash.each do |to, relation|
      a.push("#{to} (#{relation})")
    end
    list << a.join(", ") + "\n"
  end
  list
end
dump_matrix(*arg) click to toggle source

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.

This method internally calls #to_matrix method. Read documents of #to_matrix for important informations.

# File lib/bio/pathway.rb, line 274
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() click to toggle source

Returns the number of the edges in the graph.

# File lib/bio/pathway.rb, line 172
def edges
  edges = 0
  @graph.each_value do |v|
    edges += v.size
  end
  edges
end
floyd()

Alias for the #floyd_warshall method.

Alias for: floyd_warshall
floyd_warshall() click to toggle source

Floyd-Wardshall alogrithm for solving the all-pairs shortest-paths problem on a directed graph G = (V, E).

# File lib/bio/pathway.rb, line 619
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
Also aliased as: floyd
kruskal() click to toggle source

Kruskal method for finding minimam spaninng trees

# File lib/bio/pathway.rb, line 641
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
nodes() click to toggle source

Returns the number of the nodes in the graph.

# File lib/bio/pathway.rb, line 167
def nodes
  @graph.keys.length
end
small_world() click to toggle source

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.

# File lib/bio/pathway.rb, line 405
def small_world
  freq = Hash.new(0)
  @graph.each_value do |v|
    freq[v.size] += 1
  end
  return freq
end
subgraph(list = nil) click to toggle source

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)
# File lib/bio/pathway.rb, line 343
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]
    sub_graph.graph[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() click to toggle source

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).

# 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) click to toggle source

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.

The result of this method depends on the order of Hash#each (and each_key, etc.), which may be variable with Ruby version and Ruby interpreter variations (JRuby, etc.). For a workaround to remove such dependency, you can use @index to set order of Hash keys. Note that this behavior might be changed in the future. Be careful that @index is overwritten by this method.

# File lib/bio/pathway.rb, line 196
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
  if @index.empty? then
    # assign index number for each node
    @graph.keys.each_with_index do |k, i|
      @index[k] = i
    end
  else
    # begin workaround removing depencency to order of Hash#each
    # assign index number from the preset @index
    indices = @index.to_a
    indices.sort! { |i0, i1| i0[1] <=> i1[1] }
    indices.collect! { |i0| i0[0] }
    @index.clear
    v = 0
    indices.each do |k, i|
      if @graph[k] and !@index[k] then
        @index[k] = v; v += 1
      end
    end
    @graph.each_key do |k|
      unless @index[k] then
        @index[k] = v; v += 1
      end
    end
    # end workaround removing depencency to order of Hash#each
  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() click to toggle source

Reconstruct @relations from the adjacency list @graph.

# 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() click to toggle source

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.

# File lib/bio/pathway.rb, line 106
def undirected
  if directed?
    @undirected = true
    self.to_list
  end
end
undirected?() click to toggle source

Returns true or false respond to the internal state of the graph.

# File lib/bio/pathway.rb, line 79
def undirected?
  @undirected ? true : false
end