MO412/2021s1 - Tiago da Silva Almeida

Considering the degree correlation coefficient, which is defined as $r = \sum_{jk} \frac{jk(e_{jk}-q_jq_k)}{\sigma^2}$ with  $\sigma^2=\sum_k k^2q_k-\left[ \sum_k kq_k \right]^2$. And considering Net A and Net B in the figures below. Which topology do the Net A and B present? Net A is disassortative and Net B is assortative;  Net A is neutral and Net B is disassortative; Net A is assortative and Net B is neutral; Net A is assortative and Net B is disassortative;  None of the above;

In a free-scale network, the degrees of the biggest hub increases linearly with the system size in an anomalous regime (AR). Another regime predicts that hub size increases as $\ln{\ln{N}}$. In this case, it is an ultra-small world regime (USWR). However, may happens a critical point regime (CPR), where the double logarithm correction shrinks the distance compared to a random network. When this CPR is transpassed the size of hubs is reduced and they are less numerous, i.e., the network is now random. Based on this, which of the following networks are not distinguished between free-scale or a random network: Actor network ($\gamma=2.12$, $k_{min}=54$, P-VALUE=$0.00$); Science collaboration ($\gamma=3.35$, $k_{min}=25$, P-VALUE=$0.001$); Yeast protein interactions ($\gamma=2.89$, $k_{min}=7$, P-VALUE=$0.67$); WWW (in) ($\gamma=3.42$, $k_{min}=72$, P-VALUE=$0.13$); None of the above;