node.rb

class Node
  attr_reader :name

  def initialize(name)
    @name = name
    @descendants = []
  end

  def add_edge(descendant, weight)
    @descendants << {:node => descendant, :weight => weight}
  end

  def to_s
    "#{@name} -> [#{formatted_descendants.join(' ')}]"
  end

  private
  def formatted_descendants
    descendants = []
    @descendants.each do |descendant|
      descendants << "#{descendant[:node].name}-#{descendant[:weight]}"
    end
    descendants
  end
end

test.rb

require_relative "node"
require_relative "weighted_directed_graph"

graph = WeightedDirectedGraph.new

graph.add_node(Node.new(:a))
graph.add_node(Node.new(:b))
graph.add_node(Node.new(:c))
graph.add_node(Node.new(:d))
graph.add_node(Node.new(:e))

graph.add_edge(:a, :b, 5)
graph.add_edge(:b, :c, 4)
graph.add_edge(:c, :d, 8)
graph.add_edge(:d, :c, 8)
graph.add_edge(:d, :e, 6)
graph.add_edge(:a, :d, 5)
graph.add_edge(:c, :e, 2)
graph.add_edge(:e, :b, 3)
graph.add_edge(:a, :e, 7)

puts graph[:a] # => a -> [b-5 d-5 e-7]
puts graph[:b] # => b -> [c-4]
puts graph[:c] # => c -> [d-8 e-2]
puts graph[:d] # => d -> [c-8 e-6]
puts graph[:e] # => e -> [b-3]

weighted_directed_graph.rb

class WeightedDirectedGraph
  def initialize
    @nodes = {}
  end

  def add_node(node)
    @nodes[node.name] = node
  end

  def add_edge(from, to, weight)
    raise ArgumentError, "Both nodes need to exist" unless @nodes[from] && @nodes[to]
    @nodes[from].add_edge(@nodes[to], weight)
  end

  def [](name)
    @nodes[name]
  end
end