btj4dZddlmZddlZddlmZgdZedejddZ edejddZ ed edejd dd Z dS)zBridge-finding algorithms.)chainN)not_implemented_for)bridges has_bridges local_bridgesdirectedc#K|}|rtj|n|}tj||}t t j|}|:|tj|| }| D]9\}}||f|vr.||f|vr(|r t|||dkr3||fV:dS)a@Generate all bridges in a graph. A *bridge* in a graph is an edge whose removal causes the number of connected components of the graph to increase. Equivalently, a bridge is an edge that does not belong to any cycle. Bridges are also known as cut-edges, isthmuses, or cut arcs. Parameters ---------- G : undirected graph root : node (optional) A node in the graph `G`. If specified, only the bridges in the connected component containing this node will be returned. Yields ------ e : edge An edge in the graph whose removal disconnects the graph (or causes the number of connected components to increase). Raises ------ NodeNotFound If `root` is not in the graph `G`. NetworkXNotImplemented If `G` is a directed graph. Examples -------- The barbell graph with parameter zero has a single bridge: >>> G = nx.barbell_graph(10, 0) >>> list(nx.bridges(G)) [(9, 10)] Notes ----- This is an implementation of the algorithm described in [1]_. An edge is a bridge if and only if it is not contained in any chain. Chains are found using the :func:`networkx.chain_decomposition` function. The algorithm described in [1]_ requires a simple graph. If the provided graph is a multigraph, we convert it to a simple graph and verify that any bridges discovered by the chain decomposition algorithm are not multi-edges. Ignoring polylogarithmic factors, the worst-case time complexity is the same as the :func:`networkx.chain_decomposition` function, $O(m + n)$, where $n$ is the number of nodes in the graph and $m$ is the number of edges. References ---------- .. [1] https://en.wikipedia.org/wiki/Bridge_%28graph_theory%29#Bridge-Finding_with_Chain_Decompositions rootN) is_multigraphnxGraphchain_decompositionsetr from_iterablesubgraphnode_connected_componentcopyedgeslen)Gr multigraphHchains chain_edgesuvs Y/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/networkx/algorithms/bridges.pyrr sv""J!( qA  #AD 1 1 1Fe)&1122K  JJr21d;; < < A A C C 1 q6 $ $!Q{)B)B c!A$q'llQ..Q$JJJ cf tt||dS#t$rYdSwxYw)aDecide whether a graph has any bridges. A *bridge* in a graph is an edge whose removal causes the number of connected components of the graph to increase. Parameters ---------- G : undirected graph root : node (optional) A node in the graph `G`. If specified, only the bridges in the connected component containing this node will be considered. Returns ------- bool Whether the graph (or the connected component containing `root`) has any bridges. Raises ------ NodeNotFound If `root` is not in the graph `G`. NetworkXNotImplemented If `G` is a directed graph. Examples -------- The barbell graph with parameter zero has a single bridge:: >>> G = nx.barbell_graph(10, 0) >>> nx.has_bridges(G) True On the other hand, the cycle graph has no bridges:: >>> G = nx.cycle_graph(5) >>> nx.has_bridges(G) False Notes ----- This implementation uses the :func:`networkx.bridges` function, so it shares its worst-case time complexity, $O(m + n)$, ignoring polylogarithmic factors, where $n$ is the number of nodes in the graph and $m$ is the number of edges. r TF)nextr StopIteration)rr s rrrSsNh WQT " " "###t uus " 00rweight) edge_attrsTc#K|dur@|jD]6\}}t||t||zs||fV7dStj|||jD]\}}t||t||zsT||hfd} tj||||}|||fV[#tj$r||tdfVYwxYwdS)alIterate over local bridges of `G` optionally computing the span A *local bridge* is an edge whose endpoints have no common neighbors. That is, the edge is not part of a triangle in the graph. The *span* of a *local bridge* is the shortest path length between the endpoints if the local bridge is removed. Parameters ---------- G : undirected graph with_span : bool If True, yield a 3-tuple `(u, v, span)` weight : function, string or None (default: None) If function, used to compute edge weights for the span. If string, the edge data attribute used in calculating span. If None, all edges have weight 1. Yields ------ e : edge The local bridges as an edge 2-tuple of nodes `(u, v)` or as a 3-tuple `(u, v, span)` when `with_span is True`. Raises ------ NetworkXNotImplemented If `G` is a directed graph or multigraph. Examples -------- A cycle graph has every edge a local bridge with span N-1. >>> G = nx.cycle_graph(9) >>> (0, 8, 8) in set(nx.local_bridges(G)) True Tc2|vs|vr |||SdSN)nnbrdenodeswts r hide_edgez local_bridges..hide_edges-#V*;*;!r!S!}},4r )r$infN)rrrweighted_weight_functionshortest_path_lengthNetworkXNoPathfloat) r with_spanr$rrr/spanr-r.s @@rrrsYVG  DAq!IIAaD ) d   [ ) )!V 4 4G - -DAq!IIAaD ) -Q      -21a9MMMDQ*$$$$(---Qe ,,,,,,- - - -s+C  #C10C1r()TN) __doc__ itertoolsrnetworkxrnetworkx.utilsr__all__ _dispatchablerrrr)r rr>s' ...... 5 5 5Z  CCC! CLZ  777! 7t\""Z  X&&&;-;-;-'&! #";-;-;-r