content_image/352087.jpg
<img src='content_image/352087.jpg'>

the higher k$_{S}$ value in the plot, the stronger peak is at the non-zero value, and very few realizations end up at M = 0 even for smaller degrees. On the contrary, an origin with larger degree k , but smaller k$_{S}$ value results in a stronger peak at M = 0. These distributions converge quite well, and we can expect that nodes with small k$_{S}$ will in general result in a higher peak at M = 0. The above means that if an infection can reach a critical mass of nodes then it will eventually cover a significant part of the network. The low k -shell nodes cannot reach this critical mass so that the infection dies at the early stages, resulting to the strong peak at M = 0. On the contrary, the neighborhood of high k -shell nodes is favorable for sustaining an infection at early stages, allowing the system to reach this critical mass. 

