The Blind Watchmaker Network Figure 3. Metabolic networks and the blind watchmaker network. The first two panels show the data for real metabolic networks (the data is taken from Ref. [ma03a][ma03b]): Panel a) shows the average distribution Sn(k)T over 107 metabolic networks. This average distribution has a fat power-law tail Sn(k)T*k{c with c<2.2. Note that the nodes with only one link are fewer (by roughly a factor of 5) than the nodes with two links. The average size of these 107 networks is N<640 and M/N<5.35 b) the specific metabolic network distribution n(k) for the E.Coli bacteria (N<970 and M/ N<5.8). This network has 6 nodes with more than 100 links. Panel c) makes a direct comparison between the 107 metabolic networks in Panel a and 107 blind watchmaker networks with the same N and M. The agreement implies a common origin. Panel d) makes the same comparison between the E.Coli network and a single random blind watchmaker network for the same N and M. Apart from a general agreement (modulo the larger statistical spread inherent in comparing single networks) , the distribution of the split-off nodes are similar. Panel e) compares the average of the metabolic networks with the corresponding average of the blind watchmaker networks including a constraint decreasing the abundance of the single link node to the same average number, n(1), as for the metabolic networks (a = 0.07). The agreement is extraordinary. Panel f) makes the same comparison for the E. Coli. network (a = 0.08) again with a striking agreement. doi:10.1371/journal.pone.0001690.g003 and the corresponding network goes as follows: a link is defined by its link-ends such that an enumeration of the links is given by (1,2),(3,4)……..(M21,M) where the link ends corresponds to balls enumerated by 1,2,…,M as is illustrated in Fig. 1: The nodes correspond to boxes and the link-ends to the enumerated balls. The balls in the boxes are given a ranking by the vertical position of the balls in a box. The time-order of connections gives the ranking: earliest connection corresponds to the bottom position and the latest to the top. The existence of this time-order ranking is crucial in the following. The point is that the existence of an implicit time- ordering is an un-avoidable consequence of any sequential process. Natural selection is but one example of such a process. For simplicity we here consider undirected links. A network is then an association of link-ends where the associated link-ends form nodes. Note that this means that a node will always contain at least one link-end. This is the origin of ‘‘constrained’’ in the PLoS ONE | www.plosone.org 3 February 2008 | Volume 3 | Issue 2 | e1690