hSrSSKJr SSKrSSKJr /SQr\"S5\RS Sj55r \"S5\RS Sj55r \"S 5\"S5\R"S S 9SS j555r g)zBridge-finding algorithms.)chainN)not_implemented_for)bridges has_bridges local_bridgesdirectedc## UR5nU(a[R"U5OUn[R"X1S9n[ [ R "U55nUb3UR[R"X155R5nUR5H9upgXg4U;dMXv4U;dMU(a[XU5S:aM4Xg4v M; g7f)aGenerate 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 M/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/bridges.pyrr sv"J! qA  # #A 1Fe))&12K  JJr221; < A A C  6 $!{)Bc!$q'lQ.$J sB3C)9C)'C)cJ[[XS95 g![a gf=f)aPDecide 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 rrrSs.h WQ "# s  ""rweight) edge_attrsc#^^# USLa=URH,up4[X5[X5-(aM'X44v M. g[RR X5mURHMup4[X5[X5-(aM'X41mUU4Sjn[R "XXES9nX4U4v MO g![R a X4[S54v Mxf=f7f)aIterate 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 Tc0>UT;dUT;a T"XU5$gN)nnbrdenodeswts r hide_edge local_bridges..hide_edges #V*;!!!},)r#infN)rrrweighted_weight_functionshortest_path_lengthNetworkXNoPathfloat) r with_spanr#rrr.spanr,r-s @@rrrsVGGDAIAD ))d [[ ) )! 4GGDAIAD )) -221MD*$((-e ,,-s55C.AC. C.$C?C.#C+'C.*C++C.r')TN) __doc__ itertoolsrnetworkxrnetworkx.utilsr__all__ _dispatchablerrrr(r0rr?s . 5Z C!CLZ 7!7t\"Z X&;-'!#;-r0