Network fragmentation under random- or targeted link removal. a. We have removed the links among nodes of the FF and BF motif clusters from the original network. b. The same number of links as in (a) are removed randomly. In order to determine qualitatively the difference between removing the links of FF and BF motif cluster and randomly removing the same number of links, we have determined (c) the connectivity distribution, P(k), and (d) the clustering distribution, C(k) of the remaining networks. The distributions for random removal of links have been averaged over 5000 different samples. The solid line in panel c has slope γ = -2, and is the best fit for the random link removal. The solid line in panel d has slope τ = -2. We do not show C(k) for the network in panel a, since the clustering coefficients for all nodes by definition are zero. The deviation from the solid line in panels c,d, are caused by the TF, crp, which represent the most connected node of the network.