Table 1.

The parameters J and μ fitted for the real networks using the spin-system representation for the cyclic motifs and the exclusion degree 〈x²〉

Network	J	μ	〈x2〉 in 10% most-connected nodes
Brain	−2.2	1.10	0.93
E. coli	−1.55	−1.00	0.86
Electrical	−1.35	−∞	0.52
Yeast	−1.25	−∞	0.96
Tracert	−1.35	−∞	0.27
Foodweb	−0.80	−∞	0.79
Neuronal	−0.65	0.20	0.32
Signaling	−0.35	−0.05	0.45
FAA	0.00	−∞	0.22

A negative J rewards source and sink nodes, whereas a negative μ indicates a tendency for cycles to exclude neutral links. The rightmost column is a measure of the exclusion degree 〈x²〉 averaged for the 10% most-connected nodes.