%pylab inline
import numpy as np
from conway99 import *
Populating the interactive namespace from numpy and matplotlib
We start from an arbitrary vertex and its neighbours. These can necessarily be arranged as 7 blades of a fan; we fix a numbering with vertex 0 the centre, 1-14 its neighbours, and blade edges 1-2, 3-4, 5-6, 7-8, 9-10, 11-12, 13-14
seed15 = np.empty((15,15), dtype='int')
for i in range(15):
for j in range(15):
seed15[i,j] = 0
# 1-14 all nhbrs of 0
for i in range(1,15):
seed15[0,i] = 1
seed15[i,0] =1
# By fixing an ordering, a single representative suffices
for i in [1,3,5,7,9,11,13]:
seed15[i,i+1] = 1
seed15[i+1,i] = 1
# review
print(seed15)
plot_given_edges(seed15)
[[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0] [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0] [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0] [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0] [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0] [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0] [1 0 0 0 0 0 0 0 0 0 0 1 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]]
# Verify some details
assert len(seed15)*len(seed15) == num_known_zeros(seed15) + num_known_ones(seed15) + num_unknowns(seed15)
assert not(has_unknown_values(seed15))
assert lambda_compatible(seed15)
assert mu_compatible(seed15)
assert meets_adjacency_requirements(seed15, debug=True)
assert graph_is_valid(seed15)
(NB, as we started numbering at 0, this is our 16th vertex)
# Generate template with an additional vertex, and review
seed16 = get_supermatrix_template_first_unsat(seed15)
print(seed16)
plot_given_edges(seed16)
[[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0] [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1] [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2] [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2] [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2] [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2] [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2] [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2] [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2] [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2] [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2] [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2] [1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2] [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2] [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2] [0 1 2 2 2 2 2 2 2 2 2 2 2 2 2 0]]
# Fill in the template
%time super16 = templates_to_valid_graphs([seed16], verbose=2)
Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 1 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 1 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 1 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 1 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 1 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 1 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 1 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 1 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 1 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 1 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 1 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 2 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 2 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 2 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 2 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 2 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 2 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 2 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 2 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 2 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 2 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 3 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 3 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 3 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 3 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 3 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 3 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 3 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 3 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 3 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 4 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 4 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 4 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 4 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 4 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 4 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 4 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 4 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 5 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 5 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 5 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 5 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 5 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 5 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 5 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 6 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 6 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 6 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 6 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 6 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 6 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 7 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 7 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 7 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 7 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 7 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 8 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 8 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 8 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 8 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 9 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 9 graphs, 2 candidates Adding branch 0 candidate Branch 1 invalid Currently 9 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 10 graphs, 1 candidates Adding branch 0 candidate Adding branch 1 candidate Currently 10 graphs, 2 candidates Branch 0 yielded compatible graph Branch 1 invalid Currently 11 graphs, 1 candidates Branch 0 yielded compatible graph Branch 1 yielded compatible graph Reduces to 12 valid graphs Wall time: 104 ms
# Reduce to eliminate equivalent graphs
rep16 = reduce_mod_equivalence(super16, verbose=True)
1 reps for 1 candidates
# Turns out, there's only really one way to extend this! Let's take a look
plot_given_edges(rep16[0])
This was expected:
By mu=2 condition, as 15 is not a nhbr of 0, they have 2 mutual nhbrs
Moreover, we could have applied this at the template stage to reduce the search space.
# alternative template
seed16 = get_supermatrix_template_first_unsat(seed15, forced_edge=(15,14))
print(seed16)
plot_given_edges(seed16)
[[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0] [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1] [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2] [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2] [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2] [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2] [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2] [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2] [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2] [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2] [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2] [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2] [1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2] [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2] [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1] [0 1 2 2 2 2 2 2 2 2 2 2 2 2 1 0]]
# Fill in the template
%time super16 = templates_to_valid_graphs([seed16], verbose=2)
Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Adding branch 0 candidate Branch 1 invalid Currently 0 graphs, 1 candidates Branch 0 yielded compatible graph Branch 1 invalid Reduces to 1 valid graphs Wall time: 14 ms
# For convenience, can wrap up the templating, search, and reduction steps for a list of seed graphs
%time rep16 = find_valid_supergraphs_first_unsat([seed15], forced_edge=(15,14))
2020-04-29 15:23:19.396633: 1 seed templates generated 2020-04-29 15:23:19.408601: 1 valid graphs from templates 1 reps for 1 candidates 2020-04-29 15:23:19.408601: Reduced to 1 representatives Wall time: 12 ms
# confirm this is what we expected from the individual steps:
plot_given_edges(rep16[0])
We know one of the blades centred at vertex 1; namely 1-0-2-1.
We also have part of another, containing vertex 15.
wlog, let vertex 16 be the other vertex of that blade (we already force 1-16, so suffices to set 15-16)
%time rep17 = find_valid_supergraphs_first_unsat(rep16, forced_edge=(15,16))
2020-04-29 15:23:19.498323: 1 seed templates generated 2020-04-29 15:23:19.610058: 11 valid graphs from templates 1 reps for 1 candidates 2 reps for 11 candidates 2020-04-29 15:23:19.611021: Reduced to 2 representatives Wall time: 114 ms
Vertex 17 necessarily starts a new blade, so no forcing
%time rep18 = find_valid_supergraphs_first_unsat(rep17)
2020-04-29 15:23:19.617042: 2 seed templates generated 2020-04-29 15:23:19.885288: 20 valid graphs from templates 1 reps for 1 candidates 2 reps for 11 candidates 3 reps for 12 candidates 2020-04-29 15:23:19.887282: Reduced to 3 representatives Wall time: 270 ms
However, we can then force vertex 18 to be the other vertex of that blade
%time rep19 = find_valid_supergraphs_first_unsat(rep18, forced_edge=(17,18))
2020-04-29 15:23:19.894263: 3 seed templates generated 2020-04-29 15:23:20.292231: 27 valid graphs from templates 1 reps for 1 candidates 2 reps for 2 candidates 3 reps for 3 candidates 4 reps for 18 candidates 5 reps for 19 candidates 2020-04-29 15:23:20.294194: Reduced to 5 representatives Wall time: 402 ms
Continue in this fashion until we have all nhbrs of vertex 1, with forced fan pattern 0-2, 15-16, 17-18, 19-20, 21-22, 23-24, 25-26
%time rep20 = find_valid_supergraphs_first_unsat(rep19)
2020-04-29 15:23:20.301175: 5 seed templates generated 2020-04-29 15:23:21.095083: 40 valid graphs from templates 1 reps for 1 candidates 2 reps for 9 candidates 3 reps for 17 candidates 4 reps for 20 candidates 5 reps for 25 candidates 6 reps for 26 candidates 7 reps for 33 candidates 8 reps for 34 candidates 2020-04-29 15:23:21.100039: Reduced to 8 representatives Wall time: 801 ms
%time rep21 = find_valid_supergraphs_first_unsat(rep20, forced_edge=(19,20))
2020-04-29 15:23:21.107055: 8 seed templates generated 2020-04-29 15:23:22.314206: 56 valid graphs from templates 1 reps for 1 candidates 2 reps for 2 candidates 3 reps for 3 candidates 4 reps for 14 candidates 5 reps for 16 candidates 6 reps for 17 candidates 7 reps for 28 candidates 8 reps for 33 candidates 9 reps for 42 candidates 10 reps for 50 candidates 2020-04-29 15:23:22.320149: Reduced to 10 representatives Wall time: 1.21 s
%time rep22 = find_valid_supergraphs_first_unsat(rep21)
2020-04-29 15:23:22.327166: 10 seed templates generated 2020-04-29 15:23:24.034595: 60 valid graphs from templates 1 reps for 1 candidates 2 reps for 7 candidates 3 reps for 9 candidates 4 reps for 13 candidates 5 reps for 19 candidates 6 reps for 25 candidates 7 reps for 28 candidates 8 reps for 31 candidates 9 reps for 32 candidates 10 reps for 37 candidates 11 reps for 43 candidates 12 reps for 44 candidates 13 reps for 46 candidates 14 reps for 49 candidates 15 reps for 50 candidates 16 reps for 55 candidates 17 reps for 56 candidates 2020-04-29 15:23:24.044569: Reduced to 17 representatives Wall time: 1.72 s
%time rep23 = find_valid_supergraphs_first_unsat(rep22, forced_edge=(21,22))
2020-04-29 15:23:24.051581: 17 seed templates generated 2020-04-29 15:23:26.773858: 85 valid graphs from templates 1 reps for 1 candidates 2 reps for 2 candidates 3 reps for 3 candidates 4 reps for 10 candidates 5 reps for 12 candidates 6 reps for 13 candidates 7 reps for 20 candidates 8 reps for 22 candidates 9 reps for 27 candidates 10 reps for 35 candidates 11 reps for 42 candidates 12 reps for 43 candidates 13 reps for 50 candidates 14 reps for 60 candidates 15 reps for 70 candidates 16 reps for 76 candidates 17 reps for 81 candidates 2020-04-29 15:23:26.786828: Reduced to 17 representatives Wall time: 2.74 s
%time rep24 = find_valid_supergraphs_first_unsat(rep23)
2020-04-29 15:23:26.793806: 17 seed templates generated 2020-04-29 15:23:29.752891: 68 valid graphs from templates 1 reps for 1 candidates 2 reps for 5 candidates 3 reps for 9 candidates 4 reps for 13 candidates 5 reps for 15 candidates 6 reps for 17 candidates 7 reps for 21 candidates 8 reps for 25 candidates 9 reps for 26 candidates 10 reps for 29 candidates 11 reps for 31 candidates 12 reps for 33 candidates 13 reps for 34 candidates 14 reps for 37 candidates 15 reps for 41 candidates 16 reps for 45 candidates 17 reps for 46 candidates 18 reps for 49 candidates 19 reps for 50 candidates 20 reps for 53 candidates 21 reps for 57 candidates 22 reps for 58 candidates 23 reps for 61 candidates 24 reps for 62 candidates 25 reps for 65 candidates 26 reps for 66 candidates 2020-04-29 15:23:29.767866: Reduced to 26 representatives Wall time: 2.98 s
%time rep25 = find_valid_supergraphs_first_unsat(rep24, forced_edge=(23,24))
2020-04-29 15:23:29.775797: 26 seed templates generated 2020-04-29 15:23:33.773138: 78 valid graphs from templates 1 reps for 1 candidates 2 reps for 2 candidates 3 reps for 6 candidates 4 reps for 8 candidates 5 reps for 12 candidates 6 reps for 14 candidates 7 reps for 18 candidates 8 reps for 23 candidates 9 reps for 27 candidates 10 reps for 29 candidates 11 reps for 33 candidates 12 reps for 39 candidates 13 reps for 45 candidates 14 reps for 53 candidates 15 reps for 57 candidates 16 reps for 60 candidates 17 reps for 67 candidates 18 reps for 70 candidates 19 reps for 76 candidates 2020-04-29 15:23:33.787099: Reduced to 19 representatives Wall time: 4.01 s
%time rep26 = find_valid_supergraphs_first_unsat(rep25)
2020-04-29 15:23:33.795085: 19 seed templates generated 2020-04-29 15:23:36.668401: 38 valid graphs from templates 1 reps for 1 candidates 2 reps for 3 candidates 3 reps for 5 candidates 4 reps for 7 candidates 5 reps for 9 candidates 6 reps for 11 candidates 7 reps for 13 candidates 8 reps for 15 candidates 9 reps for 17 candidates 10 reps for 19 candidates 11 reps for 21 candidates 12 reps for 23 candidates 13 reps for 25 candidates 14 reps for 27 candidates 15 reps for 29 candidates 16 reps for 31 candidates 17 reps for 33 candidates 18 reps for 35 candidates 19 reps for 37 candidates 2020-04-29 15:23:36.678373: Reduced to 19 representatives Wall time: 2.89 s
%time rep27 = find_valid_supergraphs_first_unsat(rep26, forced_edge=(25,26))
2020-04-29 15:23:36.687311: 19 seed templates generated 2020-04-29 15:23:38.904415: 19 valid graphs from templates 1 reps for 1 candidates 2 reps for 2 candidates 3 reps for 4 candidates 4 reps for 6 candidates 5 reps for 8 candidates 6 reps for 10 candidates 7 reps for 12 candidates 8 reps for 14 candidates 9 reps for 16 candidates 10 reps for 18 candidates 11 reps for 19 candidates 2020-04-29 15:23:38.909406: Reduced to 11 representatives Wall time: 2.23 s
# Review an example
plot_given_edges(rep27[0])
Although we have multiple possible 27-vertex graphs, for each of them we know that vertex 2 has degree 2:
Thus we have precisely one blade centered at vertex 2, 2-0-1-2.
We require 6 more, and may arrange them to ensure blade edges 27-28, 29-30, 31-32, 33-34, 35-36, 37-38.
# Confirm our claim:
[vertex_degrees(a)[2] for a in rep27]
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
# Begin to saturate
%time rep28 = find_valid_supergraphs_first_unsat(rep27)
2020-04-29 15:23:53.125054: 11 seed templates generated 2020-04-29 15:24:48.721349: 1546 valid graphs from templates 1 reps for 1 candidates 2 reps for 3 candidates 3 reps for 133 candidates 4 reps for 134 candidates 5 reps for 135 candidates 6 reps for 140 candidates 7 reps for 277 candidates 8 reps for 278 candidates 9 reps for 279 candidates 10 reps for 283 candidates 11 reps for 286 candidates 12 reps for 303 candidates 13 reps for 304 candidates 14 reps for 417 candidates 15 reps for 418 candidates 16 reps for 419 candidates 17 reps for 428 candidates 18 reps for 443 candidates 19 reps for 444 candidates 20 reps for 553 candidates 21 reps for 554 candidates 22 reps for 555 candidates 23 reps for 557 candidates 24 reps for 561 candidates 25 reps for 562 candidates 26 reps for 697 candidates 27 reps for 698 candidates 28 reps for 699 candidates 29 reps for 701 candidates 30 reps for 703 candidates 31 reps for 707 candidates 32 reps for 708 candidates 33 reps for 749 candidates 34 reps for 750 candidates 35 reps for 773 candidates 36 reps for 774 candidates 37 reps for 776 candidates 38 reps for 839 candidates 39 reps for 840 candidates 40 reps for 841 candidates 41 reps for 843 candidates 42 reps for 849 candidates 43 reps for 850 candidates 44 reps for 891 candidates 45 reps for 892 candidates 46 reps for 977 candidates 47 reps for 978 candidates 48 reps for 979 candidates 49 reps for 981 candidates 50 reps for 982 candidates 51 reps for 983 candidates 52 reps for 988 candidates 53 reps for 1055 candidates 54 reps for 1056 candidates 55 reps for 1058 candidates 56 reps for 1121 candidates 57 reps for 1122 candidates 58 reps for 1123 candidates 59 reps for 1125 candidates 60 reps for 1126 candidates 61 reps for 1127 candidates 62 reps for 1132 candidates 63 reps for 1199 candidates 64 reps for 1200 candidates 65 reps for 1261 candidates 66 reps for 1262 candidates 67 reps for 1263 candidates 68 reps for 1265 candidates 69 reps for 1266 candidates 70 reps for 1267 candidates 71 reps for 1268 candidates 72 reps for 1269 candidates 73 reps for 1272 candidates 74 reps for 1365 candidates 75 reps for 1403 candidates 76 reps for 1404 candidates 77 reps for 1405 candidates 78 reps for 1407 candidates 79 reps for 1408 candidates 80 reps for 1409 candidates 81 reps for 1410 candidates 82 reps for 1411 candidates 83 reps for 1414 candidates 2020-04-29 15:24:49.082385: Reduced to 83 representatives Wall time: 56 s
vertex_degrees(rep28[0])
[14, 14, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
%time rep29 = find_valid_supergraphs(rep28, forced_edge=(27,28))
2020-04-28 17:08:49.804767: 83 seed templates generated 2020-04-28 17:15:22.354170: 9627 valid graphs from templates 1 reps for 1 candidates 2 reps for 2 candidates 3 reps for 3 candidates 4 reps for 4 candidates 5 reps for 5 candidates 6 reps for 6 candidates 7 reps for 7 candidates 8 reps for 8 candidates 9 reps for 9 candidates 10 reps for 10 candidates 11 reps for 11 candidates 12 reps for 12 candidates 13 reps for 13 candidates 14 reps for 14 candidates 15 reps for 15 candidates 16 reps for 16 candidates 17 reps for 17 candidates 18 reps for 18 candidates 19 reps for 19 candidates 20 reps for 20 candidates 21 reps for 22 candidates 22 reps for 23 candidates 23 reps for 24 candidates 24 reps for 25 candidates 25 reps for 26 candidates 26 reps for 27 candidates 27 reps for 28 candidates 28 reps for 29 candidates 29 reps for 31 candidates 30 reps for 33 candidates 31 reps for 34 candidates 32 reps for 35 candidates 33 reps for 36 candidates 34 reps for 37 candidates 35 reps for 38 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for 7231 candidates 1716 reps for 7241 candidates 1717 reps for 7242 candidates 1718 reps for 7247 candidates 1719 reps for 7252 candidates 1720 reps for 7258 candidates 1721 reps for 7265 candidates 1722 reps for 7266 candidates 1723 reps for 7350 candidates 1724 reps for 7361 candidates 1725 reps for 7366 candidates 1726 reps for 7370 candidates 1727 reps for 7377 candidates 1728 reps for 7383 candidates 1729 reps for 7385 candidates 1730 reps for 7457 candidates 1731 reps for 7460 candidates 1732 reps for 7461 candidates 1733 reps for 7462 candidates 1734 reps for 7463 candidates 1735 reps for 7464 candidates 1736 reps for 7465 candidates 1737 reps for 7470 candidates 1738 reps for 7484 candidates 1739 reps for 7485 candidates 1740 reps for 7486 candidates 1741 reps for 7494 candidates 1742 reps for 7495 candidates 1743 reps for 7496 candidates 1744 reps for 7505 candidates 1745 reps for 7507 candidates 1746 reps for 7518 candidates 1747 reps for 7519 candidates 1748 reps for 7575 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for 8372 candidates 1816 reps for 8374 candidates 1817 reps for 8377 candidates 1818 reps for 8378 candidates 1819 reps for 8382 candidates 1820 reps for 8417 candidates 1821 reps for 8418 candidates 1822 reps for 8423 candidates 1823 reps for 8424 candidates 1824 reps for 8427 candidates 1825 reps for 8461 candidates 1826 reps for 8462 candidates 1827 reps for 8471 candidates 1828 reps for 8483 candidates 1829 reps for 8487 candidates 1830 reps for 8488 candidates 1831 reps for 8489 candidates 1832 reps for 8490 candidates 1833 reps for 8491 candidates 1834 reps for 8492 candidates 1835 reps for 8493 candidates 1836 reps for 8498 candidates 1837 reps for 8499 candidates 1838 reps for 8500 candidates 1839 reps for 8501 candidates 1840 reps for 8532 candidates 1841 reps for 8533 candidates 1842 reps for 8539 candidates 1843 reps for 8540 candidates 1844 reps for 8542 candidates 1845 reps for 8549 candidates 1846 reps for 8550 candidates 1847 reps for 8551 candidates 1848 reps for 8552 candidates 1849 reps for 8563 candidates 1850 reps for 8572 candidates 1851 reps for 8573 candidates 1852 reps for 8574 candidates 1853 reps for 8584 candidates 1854 reps for 8585 candidates 1855 reps for 8595 candidates 1856 reps for 8598 candidates 1857 reps for 8599 candidates 1858 reps for 8603 candidates 1859 reps for 8604 candidates 1860 reps for 8607 candidates 1861 reps for 8608 candidates 1862 reps for 8611 candidates 1863 reps for 8614 candidates 1864 reps for 8617 candidates 1865 reps for 8618 candidates 1866 reps for 8622 candidates 1867 reps for 8625 candidates 1868 reps for 8628 candidates 1869 reps for 8629 candidates 1870 reps for 8632 candidates 1871 reps for 8635 candidates 1872 reps for 8650 candidates 1873 reps for 8651 candidates 1874 reps for 8653 candidates 1875 reps for 8654 candidates 1876 reps for 8657 candidates 1877 reps for 8692 candidates 1878 reps for 8694 candidates 1879 reps for 8695 candidates 1880 reps for 8699 candidates 1881 reps for 8700 candidates 1882 reps for 8703 candidates 1883 reps for 8704 candidates 1884 reps for 8705 candidates 1885 reps for 8706 candidates 1886 reps for 8711 candidates 1887 reps for 8721 candidates 1888 reps for 8722 candidates 1889 reps for 8770 candidates 1890 reps for 8771 candidates 1891 reps for 8816 candidates 1892 reps for 8817 candidates 1893 reps for 8838 candidates 1894 reps for 8882 candidates 1895 reps for 8885 candidates 1896 reps for 8923 candidates 1897 reps for 8934 candidates 1898 reps for 8937 candidates 1899 reps for 8938 candidates 1900 reps for 8942 candidates 1901 reps for 8947 candidates 1902 reps for 8948 candidates 1903 reps for 8949 candidates 1904 reps for 8950 candidates 1905 reps for 8951 candidates 1906 reps for 8955 candidates 1907 reps for 9035 candidates 1908 reps for 9036 candidates 1909 reps for 9045 candidates 1910 reps for 9057 candidates 1911 reps for 9058 candidates 1912 reps for 9060 candidates 1913 reps for 9061 candidates 1914 reps for 9062 candidates 1915 reps for 9063 candidates 1916 reps for 9066 candidates 1917 reps for 9067 candidates 1918 reps for 9068 candidates 1919 reps for 9071 candidates 1920 reps for 9072 candidates 1921 reps for 9076 candidates 1922 reps for 9079 candidates 1923 reps for 9081 candidates 1924 reps for 9082 candidates 1925 reps for 9083 candidates 1926 reps for 9084 candidates 1927 reps for 9095 candidates 1928 reps for 9101 candidates 1929 reps for 9104 candidates 1930 reps for 9105 candidates 1931 reps for 9106 candidates 1932 reps for 9112 candidates 1933 reps for 9113 candidates 1934 reps for 9116 candidates 1935 reps for 9117 candidates 1936 reps for 9160 candidates 1937 reps for 9161 candidates 1938 reps for 9171 candidates 1939 reps for 9180 candidates 1940 reps for 9181 candidates 1941 reps for 9187 candidates 1942 reps for 9188 candidates 1943 reps for 9279 candidates 1944 reps for 9280 candidates 1945 reps for 9301 candidates 1946 reps for 9307 candidates 1947 reps for 9312 candidates 1948 reps for 9390 candidates 1949 reps for 9401 candidates 1950 reps for 9406 candidates 1951 reps for 9408 candidates 1952 reps for 9417 candidates 1953 reps for 9420 candidates 1954 reps for 9517 candidates 1955 reps for 9519 candidates 1956 reps for 9528 candidates 1957 reps for 9529 candidates 1958 reps for 9531 candidates 1959 reps for 9608 candidates 1960 reps for 9609 candidates 1961 reps for 9618 candidates 2020-04-28 17:16:01.868490: Reduced to 1961 representatives Wall time: 7min 12s
%time rep30 = find_valid_supergraphs(rep29)
2020-04-28 17:20:47.337324: 1961 seed templates generated 2020-04-28 20:30:44.488288: 193030 valid graphs from templates 1 reps for 1 candidates 2 reps for 2 candidates 3 reps for 3 candidates 4 reps for 13 candidates 5 reps for 14 candidates 6 reps for 93 candidates 7 reps for 94 candidates 8 reps for 104 candidates 9 reps for 105 candidates 10 reps for 183 candidates 11 reps for 184 candidates 12 reps for 185 candidates 13 reps for 193 candidates 14 reps for 195 candidates 15 reps for 196 candidates 16 reps for 274 candidates 17 reps for 275 candidates 18 reps for 276 candidates 19 reps for 277 candidates 20 reps for 278 candidates 21 reps for 279 candidates 22 reps for 293 candidates 23 reps for 294 candidates 24 reps for 295 candidates 25 reps for 296 candidates 26 reps for 297 candidates 27 reps for 303 candidates 28 reps for 305 candidates 29 reps for 307 candidates 30 reps for 317 candidates 31 reps for 318 candidates 32 reps for 366 candidates 33 reps for 367 candidates 34 reps 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for 569 candidates 72 reps for 572 candidates 73 reps for 573 candidates 74 reps for 641 candidates 75 reps for 643 candidates 76 reps for 644 candidates 77 reps for 713 candidates 78 reps for 714 candidates 79 reps for 733 candidates 80 reps for 735 candidates 81 reps for 736 candidates 82 reps for 753 candidates 83 reps for 757 candidates 84 reps for 825 candidates 85 reps for 826 candidates 86 reps for 827 candidates 87 reps for 828 candidates 88 reps for 829 candidates 89 reps for 835 candidates 90 reps for 837 candidates 91 reps for 838 candidates 92 reps for 846 candidates 93 reps for 847 candidates 94 reps for 848 candidates 95 reps for 849 candidates 96 reps for 900 candidates 97 reps for 901 candidates 98 reps for 909 candidates 99 reps for 917 candidates 100 reps for 919 candidates 101 reps for 1007 candidates 102 reps for 1008 candidates 103 reps for 1009 candidates 104 reps for 1010 candidates 105 reps for 1079 candidates 106 reps for 1080 candidates 107 reps for 1081 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reps for 2783 candidates 557 reps for 2784 candidates 558 reps for 2785 candidates 559 reps for 2786 candidates 560 reps for 2787 candidates 561 reps for 2788 candidates 562 reps for 2789 candidates 563 reps for 2790 candidates 564 reps for 2791 candidates 565 reps for 2792 candidates 566 reps for 2793 candidates 567 reps for 2794 candidates 568 reps for 2795 candidates 569 reps for 2796 candidates 570 reps for 2797 candidates 571 reps for 2798 candidates 572 reps for 2799 candidates 573 reps for 2800 candidates 574 reps for 2801 candidates 575 reps for 2802 candidates 576 reps for 2803 candidates 577 reps for 2804 candidates 578 reps for 2805 candidates 579 reps for 2806 candidates 580 reps for 2807 candidates 581 reps for 2808 candidates 582 reps for 2809 candidates 583 reps for 2811 candidates 584 reps for 2812 candidates 585 reps for 2813 candidates 586 reps for 2814 candidates 587 reps for 2815 candidates 588 reps for 2816 candidates 589 reps for 2817 candidates 590 reps for 2818 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for 192891 candidates 122013 reps for 192892 candidates 122014 reps for 192893 candidates 122015 reps for 192894 candidates 122016 reps for 192895 candidates 122017 reps for 192896 candidates 122018 reps for 192897 candidates 122019 reps for 192898 candidates 122020 reps for 192899 candidates 122021 reps for 192900 candidates 122022 reps for 192901 candidates 122023 reps for 192902 candidates 122024 reps for 192903 candidates 122025 reps for 192904 candidates 122026 reps for 192905 candidates 122027 reps for 192906 candidates 122028 reps for 192907 candidates 122029 reps for 192908 candidates 122030 reps for 192909 candidates 122031 reps for 192910 candidates 122032 reps for 192911 candidates 122033 reps for 192912 candidates 122034 reps for 192913 candidates 122035 reps for 192914 candidates 122036 reps for 192915 candidates 122037 reps for 192916 candidates 122038 reps for 192917 candidates 122039 reps for 192918 candidates 122040 reps for 192919 candidates 122041 reps for 192920 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122071 reps for 192950 candidates 122072 reps for 192951 candidates 122073 reps for 192952 candidates 122074 reps for 192953 candidates 122075 reps for 192954 candidates 122076 reps for 192955 candidates 122077 reps for 192956 candidates 122078 reps for 192957 candidates 122079 reps for 192958 candidates 122080 reps for 192959 candidates 122081 reps for 192960 candidates 122082 reps for 192961 candidates 122083 reps for 192962 candidates 122084 reps for 192963 candidates 122085 reps for 192964 candidates 122086 reps for 192965 candidates 122087 reps for 192966 candidates 122088 reps for 192967 candidates 122089 reps for 192968 candidates 122090 reps for 192969 candidates 122091 reps for 192970 candidates 122092 reps for 192971 candidates 122093 reps for 192972 candidates 122094 reps for 192973 candidates 122095 reps for 192974 candidates 122096 reps for 192975 candidates 122097 reps for 192976 candidates 122098 reps for 192977 candidates 122099 reps for 192978 candidates 122100 reps for 192979 candidates 122101 reps for 192980 candidates 122102 reps for 192981 candidates 122103 reps for 192982 candidates 122104 reps for 192983 candidates 122105 reps for 192984 candidates 122106 reps for 192985 candidates 122107 reps for 192986 candidates 122108 reps for 192987 candidates 122109 reps for 192988 candidates 122110 reps for 192989 candidates 122111 reps for 192990 candidates 122112 reps for 192991 candidates 122113 reps for 192992 candidates 122114 reps for 192993 candidates 122115 reps for 192994 candidates 122116 reps for 192995 candidates 122117 reps for 192996 candidates 122118 reps for 192997 candidates 122119 reps for 192998 candidates 122120 reps for 192999 candidates 122121 reps for 193000 candidates 122122 reps for 193001 candidates 122123 reps for 193002 candidates 122124 reps for 193003 candidates 122125 reps for 193004 candidates 122126 reps for 193005 candidates 122127 reps for 193006 candidates 122128 reps for 193007 candidates 122129 reps for 193008 candidates 122130 reps for 193009 candidates 122131 reps for 193010 candidates 122132 reps for 193011 candidates 122133 reps for 193012 candidates 122134 reps for 193013 candidates 122135 reps for 193014 candidates 122136 reps for 193015 candidates 122137 reps for 193016 candidates 122138 reps for 193017 candidates 122139 reps for 193018 candidates 122140 reps for 193019 candidates 122141 reps for 193020 candidates 122142 reps for 193021 candidates 122143 reps for 193022 candidates 122144 reps for 193023 candidates 122145 reps for 193024 candidates 122146 reps for 193025 candidates 122147 reps for 193026 candidates 122148 reps for 193027 candidates 122149 reps for 193028 candidates 122150 reps for 193029 candidates 122151 reps for 193030 candidates 2020-04-29 06:25:53.159272: Reduced to 122151 representatives Wall time: 13h 5min 6s
import pickle
pickle.dump( rep30, open( "rep30.p", "wb" ) )
len(rep30)/len(rep29)
62.290158082610915