class_docstr: A `FunctionGraph` represents a subgraph bound by a set of input variables and
  a set of output variables, ie a subgraph that specifies an PyTensor function.
  The inputs list should contain all the inputs on which the outputs depend.
  `Variable`\s of type `Constant` are not counted as inputs.
  
  The `FunctionGraph` supports the replace operation which allows to replace
  a variable in the subgraph by another, e.g. replace ``(x + x).out`` by
  ``(2 * x).out``. This is the basis for optimization in PyTensor.
  
  This class is also responsible for verifying that a graph is valid
  (ie, all the dtypes and broadcast patterns are compatible with the
  way the `Variable`\s are used) and for tracking the `Variable`\s with
  a :attr:`FunctionGraph.clients` ``dict`` that specifies which `Apply` nodes
  use the `Variable`.  The :attr:`FunctionGraph.clients` field, combined with
  the :attr:`Variable.owner` and each :attr:`Apply.inputs`, allows the graph
  to be traversed in both directions.
  
  It can also be extended with new features using
  :meth:`FunctionGraph.attach_feature`.  See `Feature` for event types and
  documentation.  Extra features allow the `FunctionGraph` to verify new
  properties of a graph as it is optimized.
  
  The constructor creates a `FunctionGraph` which operates on the subgraph
  bound by the inputs and outputs sets.
  
  This class keeps lists for the inputs and outputs and modifies them
  in-place.
docstr: Update the clients of `var` with `new_clients`.
  
  Parameters
  ----------
  var : Variable
      The `Variable` to be updated.
  new_client : (Apply, int)
      A ``(node, i)`` pair such that ``node.inputs[i]`` is `var`.
docstr_tok: ["Update","the","clients","of","`","var","`","with","`","new_clients","`",".","Parameters","--","--","--","--","--","var",":","Variable","The","`","Variable","`","to","be","updated",".","new_client",":","(","Apply",",","int",")","A","``","(","node",",","i",")","``","pair","such","that","``","node.inputs","[","i","]","``","is","`","var","`","."]
code: def add_client(self, var: Variable, new_client: ClientType) -> None:
      """Update the clients of `var` with `new_clients`.
  
      Parameters
      ----------
      var : Variable
          The `Variable` to be updated.
      new_client : (Apply, int)
          A ``(node, i)`` pair such that ``node.inputs[i]`` is `var`.
  
      """
      if (
          not isinstance(new_client[0], Apply)
          and new_client[0] != "output"
      ):
          raise TypeError(
              'The first entry of `new_client` must be an `Apply` node or the string `"output"`'
          )
      self.clients[var].append(new_client)
  
imports: import time
  from collections import OrderedDict
  from collections.abc import Iterable, Sequence
  from typing import TYPE_CHECKING, Any, Literal, Optional, Union, cast
  import pytensor
  from pytensor.configdefaults import config
  from pytensor.graph.basic import Apply, AtomicVariable, Variable, applys_between, clone_get_equiv, graph_inputs, io_toposort, vars_between
  from pytensor.graph.basic import as_string
  from pytensor.graph.features import AlreadyThere, Feature, ReplaceValidate
  from pytensor.graph.utils import MetaObject, MissingInputError, TestValueError
  from pytensor.misc.ordered_set import OrderedSet
label_desc: Use image node_id 6 for calling the FunctionGraph obj's underlying member method code with example usage: obj.add_client(var, new_client) without return types