unnormalized structure constants

import networkx as nx
import numpy as np

"""
K4 = nx.complete_graph(4)
K33 = nx.complete_bipartite_graph(3, 3)
Petersen = nx.petersen_graph()
Cube = nx.hypercube_graph(3)
Heawood = nx.heawood_graph()
Pappus = nx.pappus_graph()
Coxeter = None
Tutte = nx.tutte_graph()
Dodecahedron = nx.dodecahedral_graph()
Desargues = nx.desargues_graph()
Biggs = None
Foster = None
smith1971 = [K4, K33, Petersen, Cube, Heawood, Pappus, Coxeter, Tutte, Dodecahedron, Desargues, Biggs, Foster]
"""

# intersection numbers 'iota'
K4 = [[3], [1]]
K33 = [[3, 2], [1, 3]]
Petersen = [[3, 2], [1, 1]]
Cube = [[3, 2, 1], [1, 2, 3]]
Heawood = [[3, 2, 2], [1, 1, 3]]
Pappus = [[3, 2, 2, 1], [1, 1, 2, 3]]
Coxeter = [[3, 2, 2, 1], [1, 1, 1, 2]]
Tutte = [[3, 2, 2, 2], [1, 1, 1, 3]]
Dodecahedron = [[3, 2, 1, 1, 1], [1, 1, 1, 2, 3]]
Desargues = [[3, 2, 2, 1, 1], [1, 1, 2, 2, 3]]
Biggs = [[3, 2, 2, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 3]]
Foster = [[3, 2, 2, 2, 2, 1, 1, 1], [1, 1, 1, 1, 2, 2, 2, 3]]

smith1971 = [K4, K33, Petersen, Cube, Heawood, Pappus, Coxeter, Tutte, Dodecahedron, Desargues, Biggs, Foster]

"""
From Wolfram:
    Given a distance-regular graph G with integers  b_i,c_i,i=0,...,d such that for any two vertices
    x,y in G at distance i=d(x,y), there are exactly c_i neighbors of y in G_(i-1)(x) and b_i neighbors of y in G_(i+1)(x), the sequence
        iota(gamma)={b_0,b_1,...,b_(d-1);c_1,...,c_d}
    is called the intersection array of G.
See also https://en.wikipedia.org/wiki/Distance-regular_graph.
N_ij^k = B^i_jk
"""
def intersection_array_to_unnormalized_constants(iota):
    diam = len(iota[0])
    b = lambda i: iota[0][i] if i in range(diam) else 0
    c = lambda i: iota[1][i-1] if i-1 in range(diam) else 0
    a = lambda i: b(0) - b(i) - c(i)

    B = np.zeros((diam+1, diam+1), dtype=int)
    B[0,:2] = a(0), b(0)
    for i in range(1, diam):
        B[i,i-1:i+2] = c(i), a(i), b(i)
    B[-1,-2], B[-1,-1] = c(diam), a(diam)

    N = [np.linalg.matrix_power(B, i) for i in range(diam+1)]
    return np.array(N)

#def intersection_array_to_structure_constants(iota):
#   N = intersection_array_to_unnormalized_constants(iota)

def demo(which=range(12)):
    for i in which:
        print(intersection_array_to_unnormalized_constants(smith1971[i]))

if __name__ == '__main__':
    demo()