wgdZddlZddlmZddlmZgdZejdZ dZ ed ed ejd Z ed ed ejd Z y) zI ======================= Distance-regular graphs ======================= N)not_implemented_for)diameter)is_distance_regularis_strongly_regularintersection_arrayglobal_parameterscN t|y#tj$rYywxYw)aReturns True if the graph is distance regular, False otherwise. A connected graph G is distance-regular if for any nodes x,y and any integers i,j=0,1,...,d (where d is the graph diameter), the number of vertices at distance i from x and distance j from y depends only on i,j and the graph distance between x and y, independently of the choice of x and y. Parameters ---------- G: Networkx graph (undirected) Returns ------- bool True if the graph is Distance Regular, False otherwise Examples -------- >>> G = nx.hypercube_graph(6) >>> nx.is_distance_regular(G) True See Also -------- intersection_array, global_parameters Notes ----- For undirected and simple graphs only References ---------- .. [1] Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance-Regular Graphs. New York: Springer-Verlag, 1989. .. [2] Weisstein, Eric W. "Distance-Regular Graph." http://mathworld.wolfram.com/Distance-RegularGraph.html TF)rnx NetworkXErrorGs i/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/algorithms/distance_regular.pyrrs+R1  s $$c>fdtdgzdg|zDS)aReturns global parameters for a given intersection array. Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d such that for any 2 vertices x,y in G at a distance i=d(x,y), there are exactly c_i neighbors of y at a distance of i-1 from x and b_i neighbors of y at a distance of i+1 from x. Thus, a distance regular graph has the global parameters, [[c_0,a_0,b_0],[c_1,a_1,b_1],......,[c_d,a_d,b_d]] for the intersection array [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d] where a_i+b_i+c_i=k , k= degree of every vertex. Parameters ---------- b : list c : list Returns ------- iterable An iterable over three tuples. Examples -------- >>> G = nx.dodecahedral_graph() >>> b, c = nx.intersection_array(G) >>> list(nx.global_parameters(b, c)) [(0, 0, 3), (1, 0, 2), (1, 1, 1), (1, 1, 1), (2, 0, 1), (3, 0, 0)] References ---------- .. [1] Weisstein, Eric W. "Global Parameters." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GlobalParameters.html See Also -------- intersection_array c3@K|]\}}|d|z |z |fyw)rN).0xybs r z$global_parameters..ms( CTQQ!q1 a Csr)zip)rcs` rr r Ds%R DSaS1#'-B CCdirected multigraphc t|dk(rtjdt|j }t |\}}|D]!\}}||k7rtj d|}#ttj|tfdD}i}i}|D]}|D]} || } t|| D cgc]} | || dz k(s| c} } t|| D cgc]} | || dzk(s| c} }|j| | | k7s|j| ||k7rtj d||| <| || <t|Dcgc]}|j|dc}t|Dcgc]}|j|dzdc}fS#t$r} tj d| d} ~ wwxYwcc} wcc} wcc}wcc}w)aReturns the intersection array of a distance-regular graph. Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d such that for any 2 vertices x,y in G at a distance i=d(x,y), there are exactly c_i neighbors of y at a distance of i-1 from x and b_i neighbors of y at a distance of i+1 from x. A distance regular graph's intersection array is given by, [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d] Parameters ---------- G: Networkx graph (undirected) Returns ------- b,c: tuple of lists Examples -------- >>> G = nx.icosahedral_graph() >>> nx.intersection_array(G) ([5, 2, 1], [1, 2, 5]) References ---------- .. [1] Weisstein, Eric W. "Intersection Array." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/IntersectionArray.html See Also -------- global_parameters rzGraph has no nodes.zGraph is not distance regular.c3VK|] }t|j"yw)N)maxvalues)rn path_lengths rrz%intersection_array..s#EA3{1~,,./Es&)NrzGraph is not distance regular) lenr NetworkXPointlessConceptiterdegreenextr dictall_pairs_shortest_path_lengthrKeyErrorgetrange)rr&_kknextrbintcintuvierrr!rrjr"s @rrrpsN 1v{))*?@@ !((* F &\FQ5 A:""#CD D r88;>> G = nx.cycle_graph(5) >>> nx.is_strongly_regular(G) True )rrr s rrrsj q ! 6hqkQ&66r) __doc__networkxr networkx.utilsrdistance_measuresr__all__ _dispatchablerr rrrrrr?s .' ,,^)DXZ \"B#!BLZ \"27#!27r