加权随机图模型
The weighted random graph model
摘要：
我们介绍了加权随机图（WRG）模型，它代表了加权对应的Erdos-Renyi随机图，并提供了更复杂的加权网络的基本见解。我们发现，分析的WRG的特点是几何重量分布，二项度分布和负二项强度分布。我们还准确地描述了与边缘去除和任何顺序和强度的加权子图的外观相关联的渗流相变。我们发现，即使是这个完全空的模型显示的渗流行为类似于在真正的加权网络中观察到的，这意味着边缘去除不能用来检测社区结构的经验。相比之下，聚类分析成功地揭示了WRG和真实网络之间的不同模式。
英文摘要：
We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is characterized by a geometric weight distribution, a binomial degree distribution and a negative binomial strength distribution. We also characterize exactly the percolation phase transitions associated with edge removal and with the appearance of weighted subgraphs of any order and intensity. We find that even this completely null model displays a percolation behavior similar to what observed in real weighted networks, implying that edge removal cannot be used to detect community structure empirically. By contrast, the analysis of clustering successfully reveals different patterns between the WRG and real networks.
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