idZddlZddlmZddlmZgdZedejdZ edejd Z edejd Z edejd Z d Z y) zConnected components.N)not_implemented_for)arbitrary_element)number_connected_componentsconnected_components is_connectednode_connected_componentdirectedc#Kt}t|}|D]5}||vst||t|z |}|j||7yw)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 i/var/www/html/strategist-ai/venv/lib/python3.12/site-packages/networkx/algorithms/components/connected.pyrrsUH 5D AA  D=1a#d)mQ/A KKNG s A1Ac8tdt|DS)a(Returns 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 K|]}dyw)N).0_s r z.number_connected_components..s2Qq2s )sumr)rs rrr]sp 2.q12 22ct|}|dk(rtjdttt ||k(S)aReturns 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.t|t||S)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 ##rc|j}|h}|g}|rQ|}g}|D]E}||D])}||vs|j||j|+t||k(sC|cS|rQ|S)zA fast BFS node generator)_adjaddappendr ) rrsourceadjr nextlevel thislevelrws rrr s &&C 8DI    AV (D=HHQK$$Q' (4yA~    Kr)__doc__networkxr networkx.utils.decoratorsrutilsr__all__ _dispatchablerrrr rrrrr4s9& Z H!HVZ 63!63rZ 63!63rZ 3$!3$lr