ó |£*^c@sUdZddlZdjddgƒZdddgZd „Zd „Zd „ZdS( sI ======================= Distance-regular graphs ======================= iÿÿÿÿNs s"Dheeraj M R s%Aric Hagberg tis_distance_regulartintersection_arraytglobal_parameterscCs0yt|ƒ}tSWntjk r+tSXdS(s!Returns 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 N(RtTruetnxt NetworkXErrortFalse(tGta((sx/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/distance_regular.pyRs ( c Cs„t|ƒ}|}|}|jdƒ|jddƒ|d}gt||ƒD]\}}|||^qQ}t|||gŒS(smReturn 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,c: tuple of lists Returns ------- p : list of 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 i(tlentappendtinserttzip( tbtctdtbatcatktxtytaa((sx/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/distance_regular.pyR?s&   0cCsK|jƒs|jƒr-tjddƒ‚n|jƒ}t|ƒ\}}x8|D]0\}}||kr|tjdƒ‚n|}qRWtj|ƒ}tg|D]}t||j ƒƒ^qŸƒ}i}i} x |D]} x|D]} y|| | } Wn t k rtjdƒ‚nXt g|| D]$}||| | dkr-|^q-ƒ} t g|| D]$}||| | dkrh|^qhƒ}| j | | ƒ| ksÅ|j | |ƒ|kr×tjdƒ‚n||| <| | | >> 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 sNot implemented for directed sor multiedge graphs.sGraph is not distance regular.isGraph is not distance regulari(t is_multigrapht is_directedRtNetworkxExceptiont degree_itertnextRtall_pairs_shortest_path_lengthtmaxtvaluestKeyErrorR tgettrange(Rtdegreet_Rtknextt path_lengthtntdiametertbinttcinttutvtiRR ((sx/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/distance_regular.pyRos6$     /   ;;0 (( t__doc__tnetworkxRtjoint __author__t__all__RRR(((sx/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/distance_regular.pyts    . 0