graphlib --- グラフ構造を操作する機能

ソースコード: Lib/

class graphlib.TopologicalSorter(graph=None)

ハッシュ可能 な頂点のグラフをトポロジカルソートする機能を提供します。

トポロジカル順序はグラフの頂点の線形順序で、頂点 u から 頂点 v への有向辺 u-> v 全てについて、頂点 u が頂点 v よりも前にくるような順序です。例えば、グラフの頂点が実行するタスクを表し、その辺があるタスクが別のタスクよりも前に実行されなければならないという制約を表す場合、トポロジカル順序は制約を満たすタスクの実行順序のシーケンスになります。トポロジカル順序が得られるのは、グラフが有向閉路を持たない、つまり有向非巡回グラフである場合でかつその時に限ります。

もしオプションの graph 引数が与えられた場合、その値は有向非巡回グラフを表す辞書でなければならず、辞書はそのキーがノードで、その値はキーのノードの先行ノードのイテラブルとなります(言い換えると、辞書の値はそのキーのノードを指す辺を持つノードのイテラブルです) 辺 add() メソッドを使うことで、さらにノードを追加することができます。


  • TopologicalSorter のインスタンスをオプションの初期グラフで生成します。

  • さらにノードをグラフに追加します。

  • prepare() をグラフ上で呼び出します。

  • is_active()True の間、 get_ready() によって返されたノード群をイテレートし、それらを処理します。ノードの処理が終わる都度、done() を呼び出します。

すぐにグラフのノードをソートした結果が必要で、並行性が不要な場合、便利なメソッド TopologicalSorter.static_order() を直接呼び出すことができます:

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


topological_sorter = TopologicalSorter()

# Add nodes to 'topological_sorter'...

while topological_sorter.is_active():
    for node in topological_sorter.get_ready():
        # Worker threads or processes take nodes to work on off the
        # 'task_queue' queue.

    # 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.
    node = finalized_tasks_queue.get()
add(node, *predecessors)

新しいノードとその先行ノードをグラフに追加します。 nodepredecessors のすべての要素は ハッシュ可能 でなければなりません。

同じ node 引数で複数回呼び出した場合、依存関係の集合は、それまでに指定した依存関係の和集合になります。

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.

prepare() を呼び出した後にこのメソッドを呼び出すと、ValueError を送出します。


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().


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:

if ts.is_active():


if ts:

前もって prepare() を呼び出さずにこの関数を呼び出すと ValueError を送出します。


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().


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.

前もって prepare() を呼び出さずにこの関数を呼び出すと ValueError を送出します。


Returns an iterator object which will iterate over nodes in a topological order. When using this method, prepare() and done() should not be called. This method is equivalent to:

def static_order(self):
    while self.is_active():
        node_group = self.get_ready()
        yield from 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:

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

>>> ts2 = TopologicalSorter()
>>> ts2.add(1, 0)
>>> ts2.add(3, 2, 1)
>>> 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.

Added in version 3.9.


graphlib モジュールは以下の例外クラスを定義します:

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.