new_contents: # This technique works best of the proposed subgraph is small. It does not scale
  # well if both graphs are large.
  
  import graphlab as gl
  
  def is_subgraph(subgraph, g, vert_id='__id', src_id='__src_id',
                  dst_id='__dst_id'):
      """
      Check if `sub_g` is a subgraph of `g`. `vert_id`, `src_id`, and
      `dst_id` are the column names for vertex, source, and destination vertex
      IDs.
      """
  
      subgraph_flag = True
  
      ## Check if vertices are a subset
      sf_filter = g.vertices.filter_by(subgraph.vertices[vert_id], vert_id)
      if sf_filter.num_rows() < subgraph.vertices.num_rows():
          subgraph_flag = False
  
      ## Check if edges are a subset
      sf_join = subgraph.edges.join(g.edges, on=[src_id, dst_id], how='inner')
      if sf_join.num_rows() < subgraph.edges.num_rows():
          subgraph_flag = False
  
      return subgraph_flag
  
  ## Use the function on a toy example
  g = gl.SGraph().add_vertices([gl.Vertex(i) for i in range(3)])
  g = g.add_edges([gl.Edge(0, 1), gl.Edge(0, 2)])
  
  g2 = gl.SGraph().add_vertices([gl.Vertex(i) for i in range(3)])
  g2 = g2.add_edges(gl.Edge(0, 1))
  print is_subgraph(g2, g)
  # True
  
  g2 = g2.add_edges(gl.Edge(1, 2))
  print is_subgraph(g2, g)
  # False
subject: Add how-to for checking if one graph is a subgraph of another.