content_image/341326.jpg
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). 

<img src='content_image/341326.jpg'>

The k -shell decomposition method assigns a unique k$_{S}$ value to each node, that corre- 

