different thresholds, as well. We outline some of the basic properties for these networks in Table I. II. THE k -SHELL DECOMPOSITION METHOD In order to classify the nodes into k -shells we employ the k -shell decomposition algorithm. First, we remove all nodes with degree k =1. After this first stage of pruning there may appear new nodes with k =1. We keep on pruning these nodes, as well, until all nodes with degree k =1 are removed. The removed nodes along with the links connecting them form the k$_{S}$ = 1 k -shell. Next, we repeat the pruning process in a similar way for the nodes of degree k =2 to extract the k$_{S}$ = 2 k -shell and subsequently for higher values of k until all nodes are removed. As a result, the network can be viewed as a set of adjacent k -shells (see Fig. 5). FIG. 5: The illustration of the k-shell extraction method. a, A schematic network is represented as a set of 3 successively enclosed k -shells labeled accordingly. b, Nodes with edges forming k$_{S}$ = 1 shell of the network. c, Nodes with edges forming k$_{S}$ = 2 shell of the network. d, Nodes with edges forming k$_{S}$ = 3 shell of the network. The k -shell decomposition method assigns a unique k$_{S}$ value to each node, that corre- 3