Vazquez Alexei
Department of Physics and Center for Complex Network Research, University of Notre Dame, Notre Dame, Indiana 46556, USA.
Phys Rev Lett. 2006 Jan 27;96(3):038702. doi: 10.1103/PhysRevLett.96.038702.
We study the spreading dynamics on graphs with a power law degree distribution pk approximately k-gamma, with 2<gamma<3, as an example of a branching process with a diverging reproductive number. We provide evidence that the divergence of the second moment of the degree distribution carries as a consequence a qualitative change in the growth pattern, deviating from the standard exponential growth. First, the population growth is extensive, meaning that the average number of vertices reached by the spreading process becomes of the order of the graph size in a time scale that vanishes in the large graph size limit. Second, the temporal evolution is governed by a polynomial growth, with a degree determined by the characteristic distance between vertices in the graph. These results open a path to further investigation on the dynamics on networks.
我们研究具有幂律度分布(p_k\approx k^{-\gamma})（其中(2 < \gamma < 3)）的图上的传播动力学，作为具有发散繁殖数的分支过程的一个例子。我们提供的证据表明，度分布二阶矩的发散导致增长模式发生质的变化，偏离了标准的指数增长。首先，种群增长是广泛的，这意味着在大图规模极限下消失的时间尺度内，传播过程到达的顶点平均数量变为图规模的量级。其次，时间演化由多项式增长控制，其阶数由图中顶点之间的特征距离决定。这些结果为进一步研究网络动力学开辟了一条道路。
