Table 1.

Performance of algorithm C_I with the heuristics leading to the largest compression on a set of example graphs (see graph descriptions in electronic supplementary material, table S1): size of the expression tree of the expanded Kirchhoff polynomial |Γ_E($\kappa$(G))|, size of the compressed expression tree $|{\mathit{\Gamma }}_{C_I}(\kappa (G))|$, heuristic $\mathcal{H}$, compression calculated as the ratio $|{\mathit{\Gamma }}_E(\kappa (G))|/|{\mathit{\Gamma }}_{C_I}(\kappa (G))|$, and average running time in seconds obtained from 10 runs (one run for HC4 and COXD) of KirchPy on a Dell laptop with Intel i-7 CPU@2.10 GHz and 8 GB RAM.

G	|ΓE(κ(G))|	|ΓCI(κ(G))|	$\mathcal{H}$	compression	time (s)
COLE1	157	46	2012	3.4	0.09
AMPAR	211	63	2102	3.3	0.07
MDH	1270	141	2001	9.0	0.27
ACTMYO	3561	142	3003	25.1	0.19
KNF33	15 553	940	3114	16.5	1.41
SHPIL	45 601	786	2204	58.0	1.58
GR	65 742	1280	2102	51.4	1.63
PHO5	640 513	4691	3215	136.5	10.61
RND	967 681	3281	1011	294.9	7.53
TF	38 746 801	1191	2002	32 533	1.84
HC4	679 477 249	333 599	1001	2036	1797
COXD	367 647 474 647 060 221	89 532	1010	4.1 × 1012	661