Analysis of ordered 3-point substructures in food webs

Authors:

Following [R. Milo et al. Science 298, 824 (2002)] we analyze small subnetworks of a network.
In contrast to Milo, whose interest was mainly in the network structure, we are interested also in the orientation of the structure.
We split 13 isomorphism classes (the sets of substructures formed one from other via cyclic and mirror permutations
of indices) and analyze each member of the class. We apply this approach to analyze the statistical
structural food web model [R.J. Williams, N.D. Martinez, Nature 404, 180, (2002)] and demonstrate analytically that this model (surprisingly) prohibit the most of possible 3-point substructures while they are common in empirical networks. We advertise this approach to use for analysis
of any networks, where the order of nodes is important. We present also the simple statistical model allowing to
find the frequencies of substructures analytically and to test the motif counting algorithms.

Authors: C. Guill, P. Paulau, C. Feenders, B. Blasius