Class: Bio::Pathway

Inherits:
Object show all
Defined in:
lib/bio/pathway.rb

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

GO::Ontology

Instance Attribute Summary collapse

Instance Method Summary collapse

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

#graphObject (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

#indexObject (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

#labelObject

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

#relationsObject (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 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_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 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

#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 419

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

#cliqueObject

Not implemented yet.

Raises:

  • (NotImplementedError)


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# File 'lib/bio/pathway.rb', line 370

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.

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.



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# 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) ⇒ Object

Not implemented yet.

Raises:

  • (NotImplementedError)


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# File 'lib/bio/pathway.rb', line 364

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_searchObject 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.

Note: 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 bahavior might be changed in the future.



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# File 'lib/bio/pathway.rb', line 481

def depth_first_search
  visited = {}
  timestamp = {}
  tree_edges = {}
  back_edges = {}
  cross_edges = {}
  forward_edges = {}
  count = 0

  # begin workaround removing depencency to order of Hash#each
  if @index.empty? then
    preference_of_nodes = nil
  else
    preference_of_nodes = {}.merge(@index)
    i = preference_of_nodes.values.max
    @graph.each_key do |node0|
      preference_of_nodes[node0] ||= (i += 1)
    end
  end
  # end workaround removing depencency to order of Hash#each

  dfs_visit = Proc.new { |from|
    visited[from] = true
    timestamp[from] = [count += 1]
    ary = @graph[from].keys
    # begin workaround removing depencency to order of Hash#each
    if preference_of_nodes then
      ary = ary.sort_by { |node0| preference_of_nodes[node0] }
    end
    # end workaround removing depencency to order of Hash#each
    ary.each do |to|
      if visited[to]
        if timestamp[to].size > 1
          if timestamp[from].first < timestamp[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
    timestamp[from].push(count += 1)
  }

  ary = @graph.keys
  # begin workaround removing depencency to order of Hash#each
  if preference_of_nodes then
    ary = ary.sort_by { |node0| preference_of_nodes[node0] }
  end
  # end workaround removing depencency to order of Hash#each
  ary.each do |node|
    unless visited[node]
      dfs_visit.call(node)
    end
  end
  return timestamp, tree_edges, back_edges, cross_edges, forward_edges
end

#dfs_topological_sortObject

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



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# 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) ⇒ Object

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



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# 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

#directedObject

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.

Returns:

  • (Boolean)


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# File 'lib/bio/pathway.rb', line 74

def directed?
  @undirected ? false : true
end

#dump_listObject

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.



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# 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) ⇒ 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.

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



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# 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

#edgesObject

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_warshallObject 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 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

#kruskalObject

Kruskal method for finding minimam spaninng trees



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# 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
  end
  index.sort{|x, y| y<=>x}.each do |idx|
    rel[idx, 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

#nodesObject

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_worldObject

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 405

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 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_listObject

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.

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.



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# 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_relationsObject

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

#undirectedObject

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.

Returns:

  • (Boolean)


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# File 'lib/bio/pathway.rb', line 79

def undirected?
  @undirected ? true : false
end