Figure 10

The robustness of the Krapivsky model to superlinear preference functions. α indicates the exponent of a preference function of the form f(d)=d ^α+c. d _max is the maximum degree of the generated network; \(\frac {d_{\text {max}}}{|E|}\) gives the proportion of edges that involve the maximum degree node. \(\frac {d_{\text {max}}}{|E|} = 1\) indicates a star formation. Note that there is a phase transition from scale-free to star-structured networks between α=1.0 and α=1.2. One-hundred networks with 10⁶ nodes each was generated for each value of α. Error bars indicate the 95% confidence interval.