ܛ7i dZddlZddlmZgdZej dZedej dZededej d d d d Z y) z5Functions for computing and verifying regular graphs.N)not_implemented_for) is_regular is_k_regulark_factorct|dk(rtjdtjj |}|j s/|j |tfd|j DS|j|fd|jD}|j|fd|jD}t|xr t|S)aDetermines whether a graph is regular. A regular graph is a graph where all nodes have the same degree. A regular digraph is a graph where all nodes have the same indegree and all nodes have the same outdegree. Parameters ---------- G : NetworkX graph Returns ------- bool Whether the given graph or digraph is regular. Examples -------- >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 4), (4, 1)]) >>> nx.is_regular(G) True rzGraph has no nodes.c3.K|] \}}|k(ywN).0_dd1s X/home/rose/Desktop/poly/venv/lib/python3.12/site-packages/networkx/algorithms/regular.py zis_regular..&s0xtq!27xc3.K|] \}}|k(ywr r )r r r d_ins rrzis_regular..)s8KDAqdaiKrc3.K|] \}}|k(ywr r )r r r d_outs rrzis_regular..+s;ldauzlr) lennxNetworkXPointlessConceptutilsarbitrary_element is_directeddegreeall in_degree out_degree)Gn1 in_regular out_regularrrrs @@@rrr s0 1v{))*?@@  # #A &B ==? XXb\0qxx000{{28AKK8  R ;all; :33{#33directedc@tfd|jDS)aDetermines whether the graph ``G`` is a k-regular graph. A k-regular graph is a graph where each vertex has degree k. Parameters ---------- G : NetworkX graph Returns ------- bool Whether the given graph is k-regular. Examples -------- >>> G = nx.Graph([(1, 2), (2, 3), (3, 4), (4, 1)]) >>> nx.is_k_regular(G, k=3) False c3.K|] \}}|k(ywr r )r nr ks rrzis_k_regular..Fs+($!QqAv(r)rr)r r)s `rrr/s. +!((+ ++r$ multigraphT)preserve_edge_attrs returns_graphc tfd|jDrtjd|j }g}|jD]+\}}|dz k\t |Dcgc]}||fc}r$t |d|zz Dcgc]}||f}}g nCt d|zd|zzDcgc]}||f}}t |d|zDcgc]}||fc} |j t t||jD]\} \} } |j| | fi| |j fd|D|j||j|| f.tj|d|tj|stjd|jfd |jD|D]\}} |j!|t#|} D]A} |j$| jD]\} } | | vs |j|| fi| AC|j'|z z|Scc}wcc}wcc}wcc}w) u<Compute a `k`-factor of a graph. A `k`-factor of a graph is a spanning `k`-regular subgraph. A spanning `k`-regular subgraph of `G` is a subgraph that contains each node of `G` and a subset of the edges of `G` such that each node has degree `k`. Parameters ---------- G : NetworkX graph An undirected graph. k : int The degree of the `k`-factor. matching_weight: string, optional (default="weight") Edge attribute name corresponding to the edge weight. If not present, the edge is assumed to have weight 1. Used for finding the max-weighted perfect matching. Returns ------- NetworkX graph A `k`-factor of `G`. Examples -------- >>> G = nx.Graph([(1, 2), (2, 3), (3, 4), (4, 1)]) >>> KF = nx.k_factor(G, k=1) >>> KF.edges() EdgeView([(1, 2), (3, 4)]) References ---------- .. [1] "An algorithm for computing simple k-factors.", Meijer, Henk, Yurai Núñez-Rodríguez, and David Rappaport, Information processing letters, 2009. c3.K|] \}}|kywr r )r r r r)s rrzk_factor..ts &XTQ1q5Xrz/Graph contains a vertex with degree less than kg@c3<K|]}rnD]}||f ywr r )r uvinneris_largeouters rrzk_factor..s&VAu8T!!Q8TsT)maxcardinalityweightz7Cannot find k-factor because no perfect matching existsc3BK|]}|vs|dddvs|yw)Nr )r ems rrzk_factor..s'N7aaqjQttWA=M7s  )anyrrNetworkXUnfeasiblecopyrangeadd_edges_fromzipitemsadd_edge remove_nodeappendmax_weight_matchingis_perfect_matchingremove_edges_fromedgesadd_nodeset_adjremove_nodes_from)r r)matching_weightggadgetsnodericoreouter_nneighborattrscore_setr3r4r;r5s ` @@@@rrrIsV &QXX &&##$UVV AG f $%*&M2Mq$M2 ',VQZ!^'DE'D!T1I'DDEE',QZVa'HI'H!T1I'HDI(-fa&j(AB(A1dAY(ABE UE*+*-eQtW]]_*E &G&h AJJw 2E 2+F VVV deT512+!0 qoNA ! !!Q '## E  N177NN%, eT5 4t9G#$66'?#8#8#:%8+AJJtX77$; EDL501%, HQ3EJBs3 I4 I9> I> J)r7) __doc__networkxrnetworkx.utilsr__all__ _dispatchablerrrr r$rr]s;. 4"4"4JZ ,!,0Z \"d$?[ @#![ r$