Jennifer Dunne, Neo Martinez, Richard Williams

Paper #: 02-03-010

Contrary to prior reports, we find that a set of 16 food webs, with 25 to 172 nodes, from a variety of aquatic and terrestrial ecosystems, generally display neither “small-world” nor “scale-free” topological properties. The food webs do display relatively short characteristic path lengths consistent with small-world topology. However, most food webs display less clustering than that expected in small-world networks, which appears related to the small size of food webs. The ratio of observed to random clustering coefficients across biological and nonbiological networks increases linearly with network size over 7 orders of magnitude ($r2 = 0.90$). A 1:1 clustering ratio occurs in networks with ~40 nodes. Most food webs display single-scale exponential or uniform degree distributions rather than the scale-free, power-law distributions previously reported for food webs and many other networks. Uniform degree distributions have not been reported previously for real-world networks. The failure to observe scale-free topology in most food webs appears related to the relatively small size, high connectance, and differences in the assembly of food webs compared to other real-world networks.