+ )i Rt^RIt^RIHt^RIHt.R Ot]!R4]PR44t ]!R4]PR44t ]!R4]PR44t ]!R4]PR44t R t R#) zConnected components.N)not_implemented_for)arbitrary_elementdirectedc#"\4p\V4pVF<pW19gK \W\V4, V4pVPV4VxK> R#5i)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& f/var/www/html/photoedit/myenv/lib/python3.14/site-packages/networkx/algorithms/components/connected.pyconnected_componentsrsKH 5D AA  =1#d)mQ/A KKNG s A7Ac8\R\V444#)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&"TFp^xK R#5i)N).0_s& r .number_connected_components..s21Qq1s)sumr)r s&rnumber_connected_componentsr]sp 2.q12 22c\V4pV^8Xd\P!R4h\\\ V444V8H#)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. z-Connectivity is undefined for the null graph.)rnxNetworkXPointlessConceptnextrr r s& r is_connectedr!sHf AAAv)) ;   t(+, - 22rc.\V\V4V4#)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. )rrr s&&rnode_connected_componentr#sj aQ ##rcVPpV0pV.pV'd]Tp.pVFPpW7,F-pW9gK VPV4VPV4K/ \V4V8XgKNVu# KdV#)zA fast BFS node generator)_adjaddappendr) r r sourceadjr nextlevel thislevelr ws &&& rrr su &&C 8DI   AVV=HHQK$$Q'4yA~  Kr)rrr!r#)__doc__networkxrnetworkx.utils.decoratorsrutilsr__all__ _dispatchablerrr!r#rrrrr3s9& Z H!HVZ 63!63rZ 63!63rZ 3$!3$lr