Analysing weighted networks requires modelling the binary and weighted properties simultaneously. We highlight three approaches for estimating the parameters responsible for them: econometric techniques treating topology as deterministic and statistical techniques either ensemble-averaging parameters or maximising an averaged likelihood over the topological randomness. In homogeneous models, equivalence holds; in heterogeneous network models, the local disorder breaks it, in a way reminiscent of the difference between `quenched' and `annealed' averages in the physics of disordered systems.

翻译：分析加权网络需要同时建模二元属性和加权属性。我们强调三种估计这些参数的方法：将拓扑结构视为确定性的计量经济学技术，以及将参数进行系综平均或在拓扑随机性上最大化平均似然的统计技术。在均匀模型中，等价性成立；而在异质性网络模型中，局部无序性打破了这种等价性，其方式类似于无序系统物理学中“淬火”平均与“退火”平均之间的差异。