o ]Zh@sdZddlZddlmZddlmZgdZejddZ d d Z ed ed ejd dZ ed ed ejddZ dS)zI ======================= Distance-regular graphs ======================= N)not_implemented_for)diameter)is_distance_regularis_strongly_regularintersection_arrayglobal_parameterscCs&zt|WdStjyYdSw)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 NetworkXErrorGr S/var/www/auris/lib/python3.10/site-packages/networkx/algorithms/distance_regular.pyrs )rcs$fddtdgdg|DS)aReturns global parameters for a given intersection array. Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d such that for any 2 vertices x,y in G at a distance i=d(x,y), there are exactly c_i neighbors of y at a distance of i-1 from x and b_i neighbors of y at a distance of i+1 from x. Thus, a distance regular graph has the global parameters, [[c_0,a_0,b_0],[c_1,a_1,b_1],......,[c_d,a_d,b_d]] for the intersection array [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d] where a_i+b_i+c_i=k , k= degree of every vertex. Parameters ---------- b : list c : list Returns ------- iterable An iterable over three tuples. Examples -------- >>> G = nx.dodecahedral_graph() >>> b, c = nx.intersection_array(G) >>> list(nx.global_parameters(b, c)) [(0, 0, 3), (1, 0, 2), (1, 1, 1), (1, 1, 1), (2, 0, 1), (3, 0, 0)] References ---------- .. [1] Weisstein, Eric W. "Global Parameters." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GlobalParameters.html See Also -------- intersection_array c3s*|]\}}|d|||fVqdS)rNr ).0xybr r ms(z$global_parameters..r)zip)rcr rrrDs$)rZdirectedZ multigraphc sjt|dkr tdt|}t|\}}|D]\}}||kr&td|}qtt|t fddD}ii|D]]|D]X}z|Wnt ya}ztd|d}~wwtfdd||D}tfd d||D}  ||ks | | krtd | <|<qEqAfd dt |Dfd dt |DfS) aReturns the intersection array of a distance-regular graph. Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d such that for any 2 vertices x,y in G at a distance i=d(x,y), there are exactly c_i neighbors of y at a distance of i-1 from x and b_i neighbors of y at a distance of i+1 from x. A distance regular graph's intersection array is given by, [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d] Parameters ---------- G: Networkx graph (undirected) Returns ------- b,c: tuple of lists Examples -------- >>> G = nx.icosahedral_graph() >>> nx.intersection_array(G) ([5, 2, 1], [1, 2, 5]) References ---------- .. [1] Weisstein, Eric W. "Intersection Array." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/IntersectionArray.html See Also -------- global_parameters rzGraph has no nodes.zGraph is not distance regular.c3s |] }t|VqdS)N)maxvaluesrn) path_lengthr rrsz%intersection_array..Ncs$g|]}|dkr|qSrr rirur r $z&intersection_array..cs$g|]}|dkr|qSrr rrr rr r!zGraph is not distance regularcsg|]}|dqS)rgetrj)bintr rr scsg|] }|ddqS)rrr"r$)cintr rr s) lenr ZNetworkXPointlessConceptiterdegreenextr dictZall_pairs_shortest_path_lengthrKeyErrorr#range) r r*_kZknextrverrrrr )r&r'rrrrrps< '         rcCst|o t|dkS)aReturns True if and only if the given graph is strongly regular. An undirected graph is *strongly regular* if * it is regular, * each pair of adjacent vertices has the same number of neighbors in common, * each pair of nonadjacent vertices has the same number of neighbors in common. Each strongly regular graph is a distance-regular graph. Conversely, if a distance-regular graph has diameter two, then it is a strongly regular graph. For more information on distance-regular graphs, see :func:`is_distance_regular`. Parameters ---------- G : NetworkX graph An undirected graph. Returns ------- bool Whether `G` is strongly regular. Examples -------- The cycle graph on five vertices is strongly regular. It is two-regular, each pair of adjacent vertices has no shared neighbors, and each pair of nonadjacent vertices has one shared neighbor:: >>> G = nx.cycle_graph(5) >>> nx.is_strongly_regular(G) True )rrr r r rrs5r) __doc__Znetworkxr Znetworkx.utilsrZdistance_measuresr__all__Z _dispatchablerrrrr r r rs    /,F