Comment on ‘An optimal algorithm for counting networks motifs’ [Physica A 381 (2007) 482–490]

Network motifs in a given network are small connected subnetworks that occur at significantly higher frequencies than would be expected for a random network. In their 2007 article “An optimal algorithm for counting network motifs”, Itzhack, Mogilevski, and Louzoun present an algorithm for detecting network motifs. Based on an experimental comparison with a motif detection software called FANMOD, they claim that their algorithm is “more than a thousand times faster” than any previous motif detection algorithm. We show that this claim is not correct and based on a significant flaw in the experimental setup. Once the experimental data of Itzhack et al. is corrected for this flaw, the implementation of their algorithm actually turns out to be a little slower than FANMOD for random Erdős–Rényi graphs. For random scale-free networks, the implementation of Itzhack et al. is faster only by a factor of 1.5, not the orders of magnitude claimed by Itzhack et al.