Network Enumeration

All data files available here are xz-compressed archives of text files containing encoded Network strings. The format is described in detail here:

Network format description

The following tables show the number of networks for a given number of species and reactions. Click the number to download the file of networks. The following document describes the various classes of CRNs and the methodologies used to enumerate them

CRNcount.pdf

More data will be added to the tables below as it is generated.

Table 1: All networks

	1 Reaction	2 Reactions	3 Reactions	4 Reactions	5 Reactions	6 Reactions	Total
1 Species	6	15	20	15	6	1	63
2 Species	16	225	2,044	13,755	71,344	297,115	384,499
3 Species	21	720	19,934	427,770	7,334,010 (zip: 12.4 MB, unzip: 477 MB)	103,808,387 (zip: 197 MB, unzip: 8.0 GB)	111,590,842
4 Species	22	1,171	67,257	3,328,704	135,622,844 (zip: 199 MB, unzip: 9.36 GB)		139,019,998
5 Species	22	1,375	122,939	11,223,502 (zip: 13.2 MB, unzip: 653 MB)			11,347,838
6 Species	22	1,429	158,617	21,927,791 (zip: 26.1 MB, unzip: 1.3 GB)			22,087,859
Total	109	4,935	370,811	36,921,537	143,028,204	104,105,503	284,431,099

Table 2: Genuine networks (no unused species)

	1 Reaction	2 Reactions	3 Reactions	4 Reactions	5 Reactions	6 Reactions	Total
1 Species	6	15	20	15	6	1	63
2 Species	10	210	2,024	13,740	71,338	297,114	384,436
3 Species	5	495	17,890	414,015	7,262,666 (zip: 12.5 MB, unzip: 473 MB)	103,511,272 (zip: 197 MB, unzip: 7.97 GB)	111,206,343
4 Species	1	451	47,323	2,900,934	128,328,834 (zip: 196 MB, unzip: 8.88 GB)		131,277,543
5 Species	0	204	55,682	7,894,798 (zip: 10.6 MB, unzip: 466 MB)			7,950,684
6 Species	0	54	35,678	10,704,289 (zip: 15.1 MB, unzip: 650 MB)			10,740,021
Total	22	1,429	158,617	21,927,791	135,662,844	103,808,387	261,559,090

In the fully open networks, the number of reactions refers to the number of reactions other than the flow-reactions.

Table 3: Fully open networks

	1 Reaction	2 Reactions	3 Reactions	4 Reactions	5 Reactions	6 Reactions	Total
1 Species	4	6	4	1	0	0	15
2 Species	14	169	1,312	7,514	32,956	115,258	157,223
3 Species	19	622	16,135	322,854	5,151,012 (zip: 9.1 MB, unzip: 350 MB)	67,769,910 (zip: 130 MB, unzip: 5.45 GB)	73,260,552
4 Species	20	1,059	59,379	2,840,062 (zip: 3.4 MB, unzip: 163 MB)	111,431,138 (zip: 159 MB, unzip: 7.88 GB)		114,331,658
5 Species	20	1,261	112,541	10,130,792 (zip: 13.2 MB, unzip: 653 MB)			10,244,615
6 Species	20	1,315	147,374	20,345,292 (zip: 24.3 MB, unzip: 1.22 GB)			20,494,001
Total	97	4,432	336,745	33,646,515	116,615,106	67,885,168	218,488,063

Table 4: Dynamically nontrivial networks

	2 Reactions	3 Reactions	4 Reactions	5 Reactions	6 Reactions	Total
1 Species	9	18	15	6	1	49
2 Species	28	322	5,031	41,506	221,729	268,616
3 Species	36	786	30,303	1,166,971	31,028,603 (zip: 81 MB, unzip: 2.39 GB)	32,226,699
4 Species	38	1,009	58,355	4,446,103		4,505,505
5 Species	38	1,050	70,695			71,783
6 Species	38	1,055	73,301			74,394
Total	187	4,240	237,700	5,654,586	31,250,333	37,147,046

Source Code + Binaries

To appear.