论文标题
随机网络中远程相关性的出现
Emergence of Long-Range Correlations in Random Networks
论文作者
论文摘要
我们通过使用生成功能对不相关的随机网络中巨型组件的远程度相关性进行分析分析。通过引入特征长度，我们发现巨型组件中的一对节点在特征长度内与程度相关，否则不相关。在临界点，巨型成分变成分形，特征长度分歧和负长度相关性。我们进一步提出了$ l $ dydistant节点对度的相关函数，该函数的行为是非临界区域距离的指数降低函数。相关函数在临界点附近遵守具有指数截止的幂律。 ERDőS-Rényi随机图用于确认这种关键行为。
We perform an analytical analysis of the long-range degree correlation of the giant component in an uncorrelated random network by employing generating functions. By introducing a characteristic length, we find that a pair of nodes in the giant component is negatively degree-correlated within the characteristic length and uncorrelated otherwise. At the critical point, where the giant component becomes fractal, the characteristic length diverges and the negative long-range degree correlation emerges. We further propose a correlation function for degrees of the $l$-distant node pairs, which behaves as an exponentially decreasing function of distance in the off-critical region. The correlation function obeys a power-law with an exponential cutoff near the critical point. The Erdős-Rényi random graph is employed to confirm this critical behavior.
