9iSrSSKrSSKJr SSKJr /SQr\"S5\RS55r \"S5\RS 55r \"S5\RS 55r \"S5\RS 55r S r g) zConnected components.N)not_implemented_for)arbitrary_element)number_connected_componentsconnected_components is_connectednode_connected_componentdirectedc## [5n[U5nUH7nX1;dM [X[U5- U5nURU5 Uv M9 g7f)aGenerate connected components. The connected components of an undirected graph partition the graph into disjoint sets of nodes. Each of these sets induces a subgraph of graph `G` that is connected and not part of any larger connected subgraph. A graph is connected (:func:`is_connected`) if, for every pair of distinct nodes, there is a path between them. If there is a pair of nodes for which such path does not exist, the graph is not connected (also referred to as "disconnected"). A graph consisting of a single node and no edges is connected. Connectivity is undefined for the null graph (graph with no nodes). Parameters ---------- G : NetworkX graph An undirected graph Yields ------ comp : set A set of nodes in one connected component of the graph. Raises ------ NetworkXNotImplemented If G is directed. Examples -------- Generate a sorted list of connected components, largest first. >>> G = nx.path_graph(4) >>> nx.add_path(G, [10, 11, 12]) >>> [len(c) for c in sorted(nx.connected_components(G), key=len, reverse=True)] [4, 3] If you only want the largest connected component, it's more efficient to use max instead of sort. >>> largest_cc = max(nx.connected_components(G), key=len) To create the induced subgraph of each component use: >>> S = [G.subgraph(c).copy() for c in nx.connected_components(G)] See Also -------- number_connected_components is_connected number_weakly_connected_components number_strongly_connected_components Notes ----- This function is for undirected graphs only. For directed graphs, use :func:`strongly_connected_components` or :func:`weakly_connected_components`. The algorithm is based on a Breadth-First Search (BFS) traversal and its time complexity is $O(n + m)$, where $n$ is the number of nodes and $m$ the number of edges in the graph. N)setlen _plain_bfsupdate)Gseennvcs h/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/networkx/algorithms/components/connected.pyrrsKH 5D AA  =1#d)mQ/A KKNG s A2Ac8[S[U555$)aReturns the number of connected components. The connected components of an undirected graph partition the graph into disjoint sets of nodes. Each of these sets induces a subgraph of graph `G` that is connected and not part of any larger connected subgraph. A graph is connected (:func:`is_connected`) if, for every pair of distinct nodes, there is a path between them. If there is a pair of nodes for which such path does not exist, the graph is not connected (also referred to as "disconnected"). A graph consisting of a single node and no edges is connected. Connectivity is undefined for the null graph (graph with no nodes). Parameters ---------- G : NetworkX graph An undirected graph. Returns ------- n : integer Number of connected components Raises ------ NetworkXNotImplemented If G is directed. Examples -------- >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)]) >>> nx.number_connected_components(G) 3 See Also -------- connected_components is_connected number_weakly_connected_components number_strongly_connected_components Notes ----- This function is for undirected graphs only. For directed graphs, use :func:`number_strongly_connected_components` or :func:`number_weakly_connected_components`. The algorithm is based on a Breadth-First Search (BFS) traversal and its time complexity is $O(n + m)$, where $n$ is the number of nodes and $m$ the number of edges in the graph. c3&# UHnSv M g7f)N).0_s r .number_connected_components..s21Qq1s)sumr)rs rrr]sp 2.q12 22c[U5nUS:Xa[R"S5e[[[ U555U:H$)arReturns True if the graph is connected, False otherwise. A graph is connected if, for every pair of distinct nodes, there is a path between them. If there is a pair of nodes for which such path does not exist, the graph is not connected (also referred to as "disconnected"). A graph consisting of a single node and no edges is connected. Connectivity is undefined for the null graph (graph with no nodes). Parameters ---------- G : NetworkX Graph An undirected graph. Returns ------- connected : bool True if the graph is connected, False otherwise. Raises ------ NetworkXNotImplemented If G is directed. Examples -------- >>> G = nx.path_graph(4) >>> print(nx.is_connected(G)) True See Also -------- is_strongly_connected is_weakly_connected is_semiconnected is_biconnected connected_components Notes ----- This function is for undirected graphs only. For directed graphs, use :func:`is_strongly_connected` or :func:`is_weakly_connected`. The algorithm is based on a Breadth-First Search (BFS) traversal and its time complexity is $O(n + m)$, where $n$ is the number of nodes and $m$ the number of edges in the graph. rz-Connectivity is undefined for the null graph.)r nxNetworkXPointlessConceptnextrrrs rrrsHf AAAv)) ;   t(+, - 22rc.[U[U5U5$)aReturns the set of nodes in the component of graph containing node n. A connected component is a set of nodes that induces a subgraph of graph `G` that is connected and not part of any larger connected subgraph. A graph is connected (:func:`is_connected`) if, for every pair of distinct nodes, there is a path between them. If there is a pair of nodes for which such path does not exist, the graph is not connected (also referred to as "disconnected"). A graph consisting of a single node and no edges is connected. Connectivity is undefined for the null graph (graph with no nodes). Parameters ---------- G : NetworkX Graph An undirected graph. n : node label A node in G Returns ------- comp : set A set of nodes in the component of G containing node n. Raises ------ NetworkXNotImplemented If G is directed. Examples -------- >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)]) >>> nx.node_connected_component(G, 0) # nodes of component that contains node 0 {0, 1, 2} See Also -------- connected_components Notes ----- This function is for undirected graphs only. The algorithm is based on a Breadth-First Search (BFS) traversal and its time complexity is $O(n + m)$, where $n$ is the number of nodes and $m$ the number of edges in the graph. )rr r$s rr r sj aQ ##rcURnU1nU/nU(a]Un/nUHJnX7H,nX;dM URU5 URU5 M. [U5U:XdMHUs $ U(aM]U$)zA fast BFS node generator)_adjaddappendr ) rrsourceadjr nextlevel thislevelrws rrr sz &&C 8DI   AV=HHQK$$Q'4yA~  ) Kr)__doc__networkxr!networkx.utils.decoratorsrutilsr__all__ _dispatchablerrrr rrrrr5s9& Z H!HVZ 63!63rZ 63!63rZ 3$!3$lr