标题： 在项目网络的分形模型中的可管理到不可管理的转变 显示英文标题

标题： Manageable to unmanageable transition in a fractal model of project networks

摘要： 项目网络的特点是度分布符合幂律，这一特性有助于传播。 相反，项目网络的最长路径长度随网络规模代数增长，这提高了随机干预的影响。 使用项目网络的复制-分裂模型，我提供了有说服力的证据，表明项目网络是分形网络。 节点之间的平均距离按 $\langle d\rangle \sim N^{\beta}$ 缩放，其中 $0<\beta<1$。 在距离 $d$ 内的节点平均数量 $\langle N\rangle_d$ 按 $\langle N\rangle_d\sim d^{D_f}$ 缩放，具有分形维数 $D_f=1/\beta>1$。 此外，我证明了复制-分裂网络在复制率 $q<q_c=1/2$ 时是脆弱的：对于任何小于1的站点占用概率，巨出组件的大小随着网络规模的增加而减小。 相反，它们在 $0<p_c<1$ 对 $q>q_c$ 表现出非平凡的渗流阈值，尽管平均出度随着网络规模的增加而发散。 我得出结论，由复制-分裂模型生成的项目网络对于 $q<q_c$ 是可管理的，否则是不可管理的。 显示英文摘要

摘要： Project networks are characterized by power law degree distributions, a property that is known to promote spreading. In contrast, the longest path length of project networks scales algebraically with the network size, which improves the impact of random interventions. Using the duplication-split model of project networks, I provide convincing evidence that project networks are fractal networks. The average distance between nodes scales as $\langle d\rangle \sim N^{\beta}$ with $0<\beta<1$. The average number of nodes $\langle N\rangle_d$ within a distance $d$ scales as $\langle N\rangle_d\sim d^{D_f}$, with a fractal dimension $D_f=1/\beta>1$. Furthermore, I demonstrate that the duplication-split networks are fragile for duplication rates $q<q_c=1/2$: The size of the giant out-component decreases with increasing the network size for any site occupancy probability less than 1. In contrast, they exhibit a non trivial percolation threshold $0<p_c<1$ for $q>q_c$, in spite the mean out-degree diverges with increasing the network size. I conclude the project networks generated by the duplication-split model are manageable for $q<q_c$ and unmanageable otherwise.