Fig. 3
a. The scheme illustrates two processes of a network growth in our growth models. One can find a biological explanation for these two processes in the main text. Process 1: The component C(2,1) is added to a network with the rate π. Process 2: Each node i in the network can be duplicated with the rate δi. We call the pre-existing to be duplicated node a “mother” node, while the new node is called a “daughter” node. A “daughter” node gets at least one edge linked to a “mother” node by default and inherits connections from the “mother” node to its neighbors each with the probability f. In other words, each neighbor of a “mother” node can become a neighbor of a “daughter” node with the probability f, while the edge between “mother” and “daughter” nodes is always added. The difference between the Uniform Copying Model (UCM) and the Preferential Copying Model (PCM) is in defining the duplication rates of nodes δi. In the UCM the node duplication rates are constant: δi=δ for all nodes, while in the PCM the duplication rates are linearly proportional to a node degree of the corresponding node: δi=δki where ki is a node degree of the ith node. b. We denote components with N nodes and E edges as C(N,E). This notation does not always correspond to a unique possible graph topology, for example, there is only one topology for C(2,1) while there are two for C(4,3). Components with N nodes and any possible number of edges are denoted as C(N,∗) which is the same as all components of size N