Figure 1

(Color online) The top and bottom left panels show the phase diagrams, $I\left(\lambda \right)$, for the numerical simulations (points), the annealed formalism (squares), the usual (dashed line) and the new (solid line) HMF approximation. The networks have been constructed using the configurational model as introduced in [19] with degree sequences following power-law degree distributions, $P\left(k\right)\sim k^{-\gamma }$, with $\gamma =2.2$, 2.6 and 3.0. The networks have $N=5000$ and $⟨k⟩=4$ and the statistics of the numerical simulations is made over 500 network realizations for each value of $\lambda$. Besides, the bottom right panel show the fraction of infected nodes of degree $k$, $\rho \left(k\right)$, using numerical simulations (points) and the annealed formalism for the case $\gamma =2.2$ and several values of $\lambda$. The recovery probability is set to $\mu =0.3$.Reuse & Permissions

Figure 2

(Color online) (Top) In the left we show the epidemic phase diagram $I\left(\lambda \right)$ for three BA ensembles with $⟨k⟩=4$, 10 and 20. In the right we show the fraction of infected individuals across degree-classes $\rho \left(k\right)$ for the ensemble with $⟨k⟩=4$ and for different values of $\lambda$. The points correspond to numerical simulations of the SIS dynamics on top of 500 network realizations while curves stand for the annealed approximation. The size of the networks is $N=5000$. (Bottom) Again, we show both $I\left(\lambda \right)$ (left) and $\rho \left(k\right)$ (right) for the case of adaptive growing networks when $N={10}^4$. Both results of numerically grown networks (points), averaged over 5000 realizations, and the solutions of the annealed formalism (curves) are shown. The network development is characterized by $\mu =0.3$, ${\tau }_T=1$ and $l=3$.Reuse & Permissions

Figure 3

(Color online) Accumulated degree distribution of growing adaptive networks when $N={10}^4$. The numerical results (points) and the distribution obtained from the evolution of the AAM (curves) are shown for several values of $\lambda$. The networks are grown using ${\tau }_T=1$, $l=3$ and $\mu =0.3$. Numerical results are obtained averaging over 100 network realizations for each value of $\lambda$.Reuse & Permissions