Recursive depth-first search (DFS) for traversing a graph in ruby.

dfs.rb

# Depth-first search (DFS) is an algorithm for traversing or
# searching a tree, tree structure, or graph. One starts at 
# the root (selecting some node as the root in the graph case)
# and explores as far as possible along each branch before backtracking.
#
# A graph can be represented by its adjacency matrix G,
# where G[i][j] == 1 if there is an edge between 
# vertices i and j and 0 otherwise.
#
# Below Graph in diagram http://i.imgur.com/sV1UzUn.png
G = [0,1,1,0,0,1,1], # A
    [1,0,0,0,0,0,0],
    [1,0,0,0,0,0,0],
    [0,0,0,0,1,1,0],
    [0,0,0,1,0,1,1],
    [1,0,0,1,1,0,0],
    [1,0,0,0,1,0,0]  # G

LABLES = %w(A B C D E F G)

def dfs(vertex)
  # mark v as explored
  print "#{LABLES[v]} " # visited

  # nullify the row to mark the
  # vertex as visited
  edge = 0
  while edge < G.size
    G[vertex][edge] = 0
    edge += 1
  end

  # Find unexplored edges
  edge = 0
  while edge < G.size
    # not explored and not same vertex
    if ( G[edge][vertex] != 0 && edge != vertex)
      dfs(edge)
    end
    edge += 1
  end
end

dfs(0) # Replace 0 with 1..6 to see different paths

I think you left v and forgot to replace it with vertex in line 23?