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Table 5 Equivalence classes in the SCC distributions

From: The topology of metabolic isotope labeling networks

level k s'up s'up (iso) SCC equivalence classes; notation: [SCC size] class size
1 3x 3x 4: [3]1, [4]2, [70]1, [175]1
2 263x 264x 20: [2]3, [2]4, [2]4, [3]1, [3]6, [4]6, [4]10, [5]2, [5]2, [6] 6 , [7]1, [7]3, [8]1, [10]1, [12]1, [18]1, [23]1, [50]1, [64]1, [82]1
3 5877x 6899x 16: [2]3, [2]4, [2]14, [3]15, [4]10, [4]15, [5]1, [5]3, [6] 24 , [7]2, [7]6, [8]1, [10]5, [18]1, [23]2, [50]1
4 55171x 115504x 12: [2]1, [2]1, [2]20, [3]23, [4]5, [4]14, [5]3, [6] 44 , [7]1, [7]4, [10]5, [23]1
5 104357x 608955x 8: [2]15, [3]24, [4]1, [4]6, [5]2, [6] 48 , [7]1, [10]2
6 86791x 674787x 5: [2]6, [3]19, [4]1, [5]1, [6] 32
7 45000x 223728x 3: [2]1, [3]12, [6] 12
8 15616x 26986x 2: [3]5, [6] 2
9 3305x 3305x 1: [3]1
10 144x 144x 0: -
11 1x 1x 0: -
  1. Underlined classes belong to an isomorphic SCC that transports a fragment of eight carbon atoms (cf. Fig. 7). Columns "s'up" and "s'up (iso)" give the theoretical speedup factor obtained when running the O MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaat0uy0HwzTfgDPnwy1egaryqtHrhAL1wy0L2yHvdaiqaacqWFoe=taaa@383C@ (n3) linear equation solver on the networks decomposed into SCCs and isomorphic SCCs.