ó |£*^c @süddlmZddlZddlTdjdddgƒZdd d d d d ddddg Zd„Zd„Z d„Z de d„Z de d„Zd„Zedƒd„ƒZedƒd„ƒZedƒd„ƒZedƒd„ƒZdS(iÿÿÿÿ(tgcdN(t*s s%Aric Hagberg s Dan Schult (dschult@colgate.edu)s!Ben Edwards (bedwards@cs.unm.edu)t descendantst ancestorsttopological_sortttopological_sort_recursivetis_directed_acyclic_grapht is_aperiodicttransitive_closuret antichainstdag_longest_pathtdag_longest_path_lengthcCsW|j|ƒs%tjd|ƒ‚nttj|d|ƒjƒƒt|gƒ}|S(sÒReturn all nodes reachable from `source` in G. Parameters ---------- G : NetworkX DiGraph source : node in G Returns ------- des : set() The descendants of source in G s The node %s is not in the graph.tsource(thas_nodetnxt NetworkXErrortsettshortest_path_lengthtkeys(tGR tdes((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyRs .cCsW|j|ƒs%tjd|ƒ‚nttj|d|ƒjƒƒt|gƒ}|S(sØReturn all nodes having a path to `source` in G. Parameters ---------- G : NetworkX DiGraph source : node in G Returns ------- ancestors : set() The ancestors of source in G s The node %s is not in the graph.ttarget(R RRRRR(RR tanc((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyR.s .cCsD|jƒstSyt|dtƒtSWntjk r?tSXdS(sôReturn True if the graph G is a directed acyclic graph (DAG) or False if not. Parameters ---------- G : NetworkX graph A graph Returns ------- is_dag : bool True if G is a DAG, false otherwise treverseN(t is_directedtFalseRtTrueRtNetworkXUnfeasible(R((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyRAs c Csj|jƒstjdƒ‚ntƒ}g}tƒ}|dkrQ|jƒ}nxø|D]ð}||krpqXn|g}xÌ|rG|d}||kr¨|jƒq|n|j|ƒg} xL||D]@} | |krÆ| |krötjdƒ‚n| j | ƒqÆqÆW| r |j | ƒq||j|ƒ|j |ƒ|jƒq|WqXW|rV|St t |ƒƒSdS(sÉReturn a list of nodes in topological sort order. A topological sort is a nonunique permutation of the nodes such that an edge from u to v implies that u appears before v in the topological sort order. Parameters ---------- G : NetworkX digraph A directed graph nbunch : container of nodes (optional) Explore graph in specified order given in nbunch reverse : bool, optional Return postorder instead of preorder if True. Reverse mode is a bit more efficient. Raises ------ NetworkXError Topological sort is defined for directed graphs only. If the graph G is undirected, a NetworkXError is raised. NetworkXUnfeasible If G is not a directed acyclic graph (DAG) no topological sort exists and a NetworkXUnfeasible exception is raised. Notes ----- This algorithm is based on a description and proof in The Algorithm Design Manual [1]_ . See also -------- is_directed_acyclic_graph References ---------- .. [1] Skiena, S. S. The Algorithm Design Manual (Springer-Verlag, 1998). http://www.amazon.com/exec/obidos/ASIN/0387948600/ref=ase_thealgorithmrepo/ s2Topological sort not defined on undirected graphs.iÿÿÿÿsGraph contains a cycle.N( RRRRtNonet nodes_itertpoptaddRtappendtextendtlisttreversed( RtnbunchRtseentordertexploredtvtfringetwt new_nodestn((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyRXs@+                 cs´ˆjƒstjdƒ‚n‡‡‡‡‡fd†‰tƒ‰tƒ‰g‰|dkrlˆjƒ}nx'|D]}|ˆkrsˆ|ƒqsqsW|r ˆSttˆƒƒSdS(s×Return a list of nodes in topological sort order. A topological sort is a nonunique permutation of the nodes such that an edge from u to v implies that u appears before v in the topological sort order. Parameters ---------- G : NetworkX digraph nbunch : container of nodes (optional) Explore graph in specified order given in nbunch reverse : bool, optional Return postorder instead of preorder if True. Reverse mode is a bit more efficient. Raises ------ NetworkXError Topological sort is defined for directed graphs only. If the graph G is undirected, a NetworkXError is raised. NetworkXUnfeasible If G is not a directed acyclic graph (DAG) no topological sort exists and a NetworkXUnfeasible exception is raised. Notes ----- This is a recursive version of topological sort. See also -------- topological_sort is_directed_acyclic_graph s2Topological sort not defined on undirected graphs.cs„ˆj|ƒxIˆ|D]=}|ˆkr<tjdƒ‚n|ˆkrˆ|ƒqqWˆj|ƒˆj|ƒˆj|ƒdS(NsGraph contains a cycle.(RRRtremoveR (R(R*(Rt_dfsRR'R&(sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyR.Õs     N(RRRRRRR"R#(RR$RR(((RR.RR'R&sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyR«s&       c Cs8|jƒstjdƒ‚nt|jƒƒ}id|6}|g}d}d}x‹|rßg}xh|D]`}xW||D]K}||kr­t|||||dƒ}qy|j|ƒ||| 1 that divides the length of every cycle in the graph. Parameters ---------- G : NetworkX DiGraph Graph Returns ------- aperiodic : boolean True if the graph is aperiodic False otherwise Raises ------ NetworkXError If G is not directed Notes ----- This uses the method outlined in [1]_, which runs in O(m) time given m edges in G. Note that a graph is not aperiodic if it is acyclic as every integer trivial divides length 0 cycles. References ---------- .. [1] Jarvis, J. P.; Shier, D. R. (1996), Graph-theoretic analysis of finite Markov chains, in Shier, D. R.; Wallenius, K. T., Applied Mathematical Modeling: A Multidisciplinary Approach, CRC Press. s.is_aperiodic not defined for undirected graphsiiN( RRRtnextRRR tlenRtsubgraphR( Rtstlevelst this_leveltgtlt next_leveltuR(((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyRôs*"       "  t undirectedcsstjƒ}|j|jƒƒ|j|jƒƒx:|D]2‰|j‡fd†tj|dˆƒDƒƒq9W|S(s% Returns transitive closure of a directed graph The transitive closure of G = (V,E) is a graph G+ = (V,E+) such that for all v,w in V there is an edge (v,w) in E+ if and only if there is a non-null path from v to w in G. Parameters ---------- G : NetworkX DiGraph Graph Returns ------- TC : NetworkX DiGraph Graph Raises ------ NetworkXNotImplemented If G is not directed References ---------- .. [1] http://www.ics.uci.edu/~eppstein/PADS/PartialOrder.py c3s'|]}ˆ|krˆ|fVqdS(N((t.0R8(R((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pys PsR (RtDiGraphtadd_nodes_fromRtadd_edges_fromt edges_itertdfs_preorder_nodes(RtTC((R(sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyR0s   0c csÇtj|ƒ}gtj|dtƒfg}x“|rÂ|jƒ\}}|Vxo|r¾|jƒ}||g}g|D],}|||kp™|||ksv|^qv}|j||fƒqPWq0WdS(sNGenerates antichains from a DAG. An antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable. Parameters ---------- G : NetworkX DiGraph Graph Returns ------- antichain : generator object Raises ------ NetworkXNotImplemented If G is not directed NetworkXUnfeasible If G contains a cycle Notes ----- This function was originally developed by Peter Jipsen and Franco Saliola for the SAGE project. It's included in NetworkX with permission from the authors. Original SAGE code at: https://sage.informatik.uni-goettingen.de/src/combinat/posets/hasse_diagram.py References ---------- .. [1] Free Lattices, by R. Freese, J. Jezek and J. B. Nation, AMS, Vol 42, 1995, p. 226. RN(RRRRRR ( RR@tantichains_stackst antichaintstacktxt new_antichainttt new_stack((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyR Us%    9cCsèi}xrtj|ƒD]a}g|j|D]}||dd|f^q*}|rgt|ƒ||©s(RRtpredtmaxtitemsR R"R#(RtdisttnodeR(tpairstlengtht_tpath((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyR Šs2' cCsttj|ƒƒd}|S(s=Returns the longest path length in a DAG Parameters ---------- G : NetworkX DiGraph Graph Returns ------- path_length : int Longest path length Raises ------ NetworkXNotImplemented If G is not directed See also -------- dag_longest_path i(R0RR (Rt path_length((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyR ±s(t fractionsRtnetworkxRtnetworkx.utils.decoratorstjoint __author__t__all__RRRRRRRRtnot_implemented_forRR R R (((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/dag.pyts2        SI <%5'