hSrSSKrSSKJr SSKJr /SQr\RS5r Sr \"S 5\"S 5\RS 555r \"S 5\"S 5\RS 555r g) zI ======================= Distance-regular graphs ======================= N)not_implemented_for)diameter)is_distance_regularis_strongly_regularintersection_arrayglobal_parameterscP[U5 g![Ra gf=f)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 V/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/distance_regular.pyrrs+R1  s %%c@^U4Sj[TS/-S/U-55$)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 c3D># UHupUTSU- U- U4v M g7f)rN).0xybs r $global_parameters..ms( C-BTQQ!q1 a -Bs r)zip)rcs` rr r Ds%R DSaS1#'-B CCdirected multigraphc ^[U5S:Xa[R"S5e[UR 55n[ U5up#UH"up$XC:wa[R "S5eUnM$ [[R"U55m[U4SjT55n0n0nUHnUHn TUU n [X V s/sHn TU UU S- :XdMU PM sn 5n [X V s/sHn TU UU S-:XdMU PM sn 5nURX5U :wdURX5U:wa[R "S5eXU 'XU 'M M [U5Vs/sHoRUS5PM sn[U5Vs/sHoRUS-S5PM sn4$![an [R "S5U eSn A ff=fs sn fs sn fs snfs snf)a(Returns 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.c3\># UH!n[TUR55v M# g7f)N)maxvalues)rn path_lengths rr%intersection_array..s&EA3{1~,,.//s),NrzGraph is not distance regular) lenr NetworkXPointlessConceptiterdegreenextr dictall_pairs_shortest_path_lengthr KeyErrorgetrange)rr(_kknextrbintcintuvierrr"rrjr#s @rrrpsN 1v{))*?@@ !((* F &\FQ :""#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 rrrrrrAs .' ,,^)DXZ \"B#!BLZ \"27#!27r