Complex Networks and Systems Group, ISI Foundation, Torino, Italy.
Phys Rev Lett. 2009 Oct 16;103(16):168701. doi: 10.1103/PhysRevLett.103.168701. Epub 2009 Oct 13.
We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in order to produce a scale-free graph with given exponent lambda for the degree distribution, but the choice of each new link depends on the mass of the clusters that this link will merge. Networks constructed via this biased procedure show a percolation transition which strongly differs from the one observed in standard percolation, where links are introduced just randomly. The different growth process leads to a phase transition with a nonvanishing percolation threshold already for lambda>lambda(c) approximately 2.2. More interestingly, the transition is continuous when lambda<or=3 but becomes discontinuous when lambda>3. This may have important consequences for both the structure of networks and for the dynamics of processes taking place on them.
我们研究了通过合作 Achlioptas 增长过程构建的无标度网络。为了生成具有给定幂律的度分布的无标度图，在节点之间引入了链接，但每个新链接的选择取决于该链接将合并的簇的质量。通过这种有偏差的过程构建的网络显示出渗流相变，与在标准渗流中观察到的渗流相变有很大的不同，在标准渗流中，链接只是随机引入的。不同的增长过程导致当 λ > λ(c)≈2.2 时，已经存在非零的渗流阈值的相变。更有趣的是，当 λ < or =3 时，相变是连续的，但当 λ >3 时，相变是不连续的。这对于网络的结构和在其上发生的过程的动力学都可能有重要的影响。
