Comment on "Network Motifs: Simple Building Blocks of Complex Networks" and "Superfamilies of Evolved and Designed Networks"

Quantitative analysis of the local structure of food webs

“…One can think of two principle arguments for their existence: either they are a consequence of the mechanism generating the network (Artzy- Randrup et al, 2004) or they provide some ecological advantage and have arisen as a result of selection pressure. Here we show that the generalized cascade model yields well-defined patterns of over/under-representation of motifs.…”

Uncovering a Hidden Distributed Architecture Behind Scale-free Transcriptional Regulatory Networks

“…41 It is of importance that the correct randomization procedure is employed, as an unrealistic randomization procedure can introduce bias into the estimation of statistical significance. 42 To this end, all scale-free networks for the statistical tests used in the analysis have been generated from the original transcription network by randomly rewiring the network edges between transcription factors while maintaining the out-going and in-coming degree distributions of all the transcription factors and target genes. Such a procedure ensures that the in-degree and out-degree distributions of the random networks show identical pattern of behavior as observed in the original transcriptional network.…”

Good versus optimal: Why network analytic methods need more systematic evaluation

“…The choice of Milo et al in their first paper on network motifs was to use a null-model in which the degree sequences were maintained while the edges were completely perturbed [53]. An interesting comment on their work by Artzy-Randrup et al showed that some of the network motifs that were significant with respect to that null-model were absolutely insignificant with another, geometrical null-model [4]. The main implication of their article is not that the geometrical null-model was in any way better suited as a null-model but just that the question of when which random graph model can be used as a null-model is an open question that has not been resolved until today.…”

“…A null-model in this respect is any kind of randomized network that maintains certain structural aspects of a graph. The most simple one is the classical Gilbert random graph 4 in which every edge has the same probability 0 p 1 to be established. Given a graph G = (V, E), the according random graph is built on the same number of nodes n = |V| and p is defined such that the expected number of edges equals m |E|:…”