# graphlib — Functionality to operate with graph-like structures

Source code: Lib/graphlib.py

`class graphlib.TopologicalSorter(graph=None)`

Provides functionality to topologically sort a graph of hashable nodes.

A topological order is a linear ordering of the vertices in a graph such that for every directed edge u -> v from vertex u to vertex v, vertex u comes before vertex v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this example, a topological ordering is just a valid sequence for the tasks. A complete topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph.

If the optional graph argument is provided it must be a dictionary representing a directed acyclic graph where the keys are nodes and the values are iterables of all predecessors of that node in the graph (the nodes that have edges that point to the value in the key). Additional nodes can be added to the graph using the `add()` method.

In the general case, the steps required to perform the sorting of a given graph are as follows:

In case just an immediate sorting of the nodes in the graph is required and no parallelism is involved, the convenience method `TopologicalSorter.static_order()` can be used directly:

pycon3
```>>> graph = {"D": {"B", "C"}, "C": {"A"}, "B": {"A"}}
>>> ts = TopologicalSorter(graph)
>>> tuple(ts.static_order())
('A', 'C', 'B', 'D')```

The class is designed to easily support parallel processing of the nodes as they become ready. For instance:

Python
```topological_sorter = TopologicalSorter()

topological_sorter.prepare()
while topological_sorter.is_active():
# Worker threads or processes take nodes to work on off the

# When the work for a node is done, workers put the node in
# 'finalized_tasks_queue' so we can get more nodes to work on.
# The definition of 'is_active()' guarantees that, at this point, at
# least one node has been placed on 'task_queue' that hasn't yet
# been passed to 'done()', so this blocking 'get()' must (eventually)
# succeed.  After calling 'done()', we loop back to call 'get_ready()'
# again, so put newly freed nodes on 'task_queue' as soon as
# logically possible.
topological_sorter.done(node)```
`add(node, *predecessors)`

Add a new node and its predecessors to the graph. Both the node and all elements in predecessors must be hashable.

If called multiple times with the same node argument, the set of dependencies will be the union of all dependencies passed in.

It is possible to add a node with no dependencies (predecessors is not provided) or to provide a dependency twice. If a node that has not been provided before is included among predecessors it will be automatically added to the graph with no predecessors of its own.

Raises `ValueError` if called after `prepare()`.

`prepare()`

Mark the graph as finished and check for cycles in the graph. If any cycle is detected, `CycleError` will be raised, but `get_ready()` can still be used to obtain as many nodes as possible until cycles block more progress. After a call to this function, the graph cannot be modified, and therefore no more nodes can be added using `add()`.

`is_active()`

Returns `True` if more progress can be made and `False` otherwise. Progress can be made if cycles do not block the resolution and either there are still nodes ready that haven’t yet been returned by `TopologicalSorter.get_ready()` or the number of nodes marked `TopologicalSorter.done()` is less than the number that have been returned by `TopologicalSorter.get_ready()`.

The `__bool__()` method of this class defers to this function, so instead of:

Python
```if ts.is_active():
...```

it is possible to simply do:

Python
```if ts:
...```

Raises `ValueError` if called without calling `prepare()` previously.

`done(*nodes)`

Marks a set of nodes returned by `TopologicalSorter.get_ready()` as processed, unblocking any successor of each node in nodes for being returned in the future by a call to `TopologicalSorter.get_ready()`.

Raises `ValueError` if any node in nodes has already been marked as processed by a previous call to this method or if a node was not added to the graph by using `TopologicalSorter.add()`, if called without calling `prepare()` or if node has not yet been returned by `get_ready()`.

`get_ready()`

Returns a `tuple` with all the nodes that are ready. Initially it returns all nodes with no predecessors, and once those are marked as processed by calling `TopologicalSorter.done()`, further calls will return all new nodes that have all their predecessors already processed. Once no more progress can be made, empty tuples are returned.

Raises `ValueError` if called without calling `prepare()` previously.

`static_order()`

Returns an iterable of nodes in a topological order. Using this method does not require to call `TopologicalSorter.prepare()` or `TopologicalSorter.done()`. This method is equivalent to:

Python
```def static_order(self):
self.prepare()
while self.is_active():
yield from node_group
self.done(*node_group)```

The particular order that is returned may depend on the specific order in which the items were inserted in the graph. For example:

pycon3
```>>> ts = TopologicalSorter()
>>> print([*ts.static_order()])
[2, 0, 1, 3]

>>> ts2 = TopologicalSorter()
>>> print([*ts2.static_order()])
[0, 2, 1, 3]```

This is due to the fact that “0” and “2” are in the same level in the graph (they would have been returned in the same call to `get_ready()`) and the order between them is determined by the order of insertion.

If any cycle is detected, `CycleError` will be raised.

New in version 3.9.

## Exceptions

The `graphlib` module defines the following exception classes:

`exception graphlib.CycleError`

Subclass of `ValueError` raised by `TopologicalSorter.prepare()` if cycles exist in the working graph. If multiple cycles exist, only one undefined choice among them will be reported and included in the exception.

The detected cycle can be accessed via the second element in the `args` attribute of the exception instance and consists in a list of nodes, such that each node is, in the graph, an immediate predecessor of the next node in the list. In the reported list, the first and the last node will be the same, to make it clear that it is cyclic.