Assessing the statistical significance of network patterns is crucial for understanding whether such patterns indicate the presence of interesting network phenomena, or whether they simply result from less interesting processes, such as nodal-heterogeneity. Typically, significance is computed with reference to a null model. While there has been extensive research into such null models for unweighted graphs, little has been done for the weighted case. This article suggests a null model for weighted graphs. The model fixes node strengths exactly, and approximately fixes node degrees. A novel MCMC algorithm is proposed for sampling the model, and its stochastic stability is considered. We show empirically that the model compares favorably to alternatives, particularly when network patterns are subtle. We show how the algorithm can be used to evaluate the statistical significance of community structure.

翻译：评估网络模式的统计意义,对于了解这种模式是否表明存在有趣的网络现象,或者它们是否仅仅是由不那么有趣的过程,例如交点异质性,例如交点异质性,至关重要。通常,根据一个无效模型来计算其重要性。虽然对未加权图案的这种无效模型进行了广泛的研究,但对于加权图案却没有做多少工作。本条建议加权图案的无效模型。模型精确地固定节点强度,大约固定节点度。提议采用新的MCMC算法对模型进行取样,并考虑其随机稳定性。我们从经验上表明,模型优于替代方法,特别是在网络模式微妙的情况下。我们展示了如何使用算法来评估共同体结构的统计意义。