o h@sdZddlmZddlZddlmZgdZedejdddZ edejdd d Z ed edejd d dddZ dS)zBridge-finding algorithms.)chainN)not_implemented_for)bridges has_bridges local_bridgesdirectedccs|}|r t|n|}tj||d}tt|}|dur+|t|| }| D]"\}}||f|vrQ||f|vrQ|rLt |||dkrLq/||fVq/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_edgesuvro/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/networkx/algorithms/bridges.pyr s; rcCs,z tt||dWdStyYdSw)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. rFT)nextr StopIteration)rr rrrrSs 4 rrweight) edge_attrsTc #s|dur |jD]\}}t||t||@s||fVqdStj|||jD]?\}}t||t||@si||hfdd}ztj||||d}|||fVWq*tjyh||tdfVYq*wq*dS)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 Tcs |vs|vr|||SdSNr)nnbrdenodeswtrr hide_edges z local_bridges..hide_edge)r!infN)rrr weighted_weight_functionshortest_path_lengthNetworkXNoPathfloat)r with_spanr!rrr*spanrr'rrs(+ rr#)TN) __doc__ itertoolsrnetworkxr networkx.utilsr__all__ _dispatchablerrrrrrrs  F: