Fig. 5
From: Metric clusters in evolutionary games on scale-free networks
The impact of heterogeneity and clustering. a–c Final (after 2 × 105 update steps) density of cooperators (color coded) for the prisoner’s dilemma game (T = 1.5 and S = −0.5) averaged over 50 realizations as a function of the degree distribution power-law exponent γ and mean local clustering \(\bar c\). Networks have N = 2 × 104 nodes and a mean degree \(\left\langle k \right\rangle\) ≈ 6. The initial density of cooperators is always c(0) = 0.5. a Randomly assigned initial cooperators. b Hubs are assigned as initial cooperators with a probability p ∝ k. c Initial cooperators are localized in the angular space. d Regions where the final cooperation exceeds a threshold value of 0.3 for the cases presented in a–c. e Final cooperation as a function of the network heterogeneity for different values of \(\bar c\) starting with preferential hub assignment, representing different cuts through b. Error bars denote one standard deviation from top to bottom. f Final cooperation as a function of the network heterogeneity for different values of \(\bar c\) starting with cooperators assigned into a metric cluster, representing different cuts through c. Error bars denote one standard deviation from top to bottom. g Final cooperation density as a function of the network size for synthetic networks with power-law exponent γ = 2.9, \(\bar c = 0.6\), and mean degree \(\left\langle k \right\rangle\) ≈ 6. Error bars denote one standard deviation from top to bottom. h Final cooperation for different network sizes (see legend) and the same parameters as before. Initial cooperators (c(0) = 0.5) are assigned into different numbers of disjoint metric clusters, whose number is plotted on the x-axis. i The same as h, but on the x-axis the resulting absolute size of each cluster is shown, given by the number of nodes divided by twice the number of cooperating clusters
