networkx.algorithms.distance_regular.global_parameters¶

global_parameters(b, c)[source]¶

Returns 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

An iterable over three tuples.

Return type

iterable

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