Figure 1. The mapping between network and the balls-in- boxes model. The left half shows a network of nodes and links with the link-ends enumerated. The right half shows the equivalent balls-in- boxes model. The vertical position of the balls in a box gives the order in which they arrived into the box, or more generally a ranking. doi:10.1371/journal.pone.0001690.g001 the two split off nodes with the largest k. The bulk part of the N(k)- distribution of E. Coli. is broad and power law like. The straight line in the figure corresponds to N(k),k2c with c$2 and illustrates The Blind Watchmaker Network that the node-degree distribution for metabolic networks is broad and power-law like, as was first demonstrated in Ref. [16]. This power law like distribution is even more pronounced when taking an average over many different metabolic networks as shown in Fig. 3(a). As the complex metabolic system is projected and reduced into a network, the relevant possibilities also reduce to the correspond- ing relevant possibilities of the network. A possible state of a network corresponds to a possible way of assembling its parts i.e. it includes both a description of what nodes a particular node is connected to and a description of the time order this particular node was connected to these other nodes. The blind watchmaker network is the network which is unbiased with respect to these different assembling possibilities. In the following we will briefly explain what the properties of the blind watchmaker network are and how they are obtained (with more details in supporting information in Text S1). Results We start from a simplified network model, the constrained-balls- in-boxes(CBB)-model [17]. The mapping between the CBB-model Figure 2. The most unbiased box(node)-size distribution. Panels a-d show the most unbiased distributions n(k) obtained by the algorithm method: a) The variational solution n(k) = A exp(2bk)/k for the statistical states of the CBB-model compared to the average Sn(k)T solution from the algorithm method in case of N = 1000 and M/N = 4. The fact that the two solutions agree reflects that the algorithm contains the least possible information compatible with the constraints: b) The same thing for the blind watchmaker version of the CBB-model. In this case the variational solution is n(k) = A exp(2bk)/k2 and the agreement again reflects that no additional information is contained in the algorithm. The two curves in the panel corresponds to N = 1000 and M/N = 2 and 4, respectively. As seen the distribution becomes more power law like with increasing ratio M=N~SkT : c) The corresponding network solution. The most unbiased solution in this case gives the blind watchmaker network structure. The variational solution cannot be simply obtained for the network case because of the network constraints. By contrast these constraints are easily incorporated into the algorithm method. The panel shows the average solution for M/N = 4 and N = 1000. The solution has a fat tail power law n(k),k2c with c<2.1 : d) A real network is just one representation n(k) and not an average Sn(k)T. The panel shows a single network for N = 1000 and M/N = 4. A single network always contain large split-off nodes. doi:10.1371/journal.pone.0001690.g002 PLoS ONE | www.plosone.org 2 February 2008 | Volume 3 | Issue 2 | e1690