Computing paths and cycles in biological interaction graphs

Table 1 Benchmarks for path and cycle enumeration

Network	Nodes	Edges	Enumeration of cycles			Enumeration of input-output paths
			Number of cycles	EMC	Johnson	Number of I/O paths	EMC	Breadth-first
				[s]	[s]		[s]	[s]
T-cell	94	138	100	0.1	0.04	8058	0.98	0.27
EGFR	106	230	237	0.15	0.07	384766	131	21
T-cell+EGFR	200	410	337	6.0 ± 0.9	0.14 ± 0.01	n/a	n/a	n/a
Regulon DB	1493	3565	132	194	0.77	44194	4716	38
CA1 neuron	512	1047	n/a	n/a	n/a	n/a	n/a	n/a
Cancer signaling	1240	3144	n/a	n/a	n/a	n/a	n/a	n/a

The running times when using elementary modes computation (columns "EMC") are compared with those of the graph-algorithms (Johnson's algorithm and breadth-first search, respectively). The number of edges refers to unique edges (parallel edges with the same sign and half-edges are removed before calculation). The values for the combined network "T-cell+EGFR" are mean and standard error over ten runs with different random connections between the two networks. An entry n/a indicates that the procedure quickly ran out of memory (3 GB) because of a combinatorial explosion of paths or cycles. The platform used was MATLAB 2006 b under 32 bit Linux with an Intel E6600 processor.