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Weights and directionality of the edges carry a large part of the informationwe can extract from a complex network. However, many network measures wereformulated initially for undirected binary networks. The necessity toincorporate information about the weights led to the conception of the multipleextensions, particularly for definitions of the local clustering coefficientdiscussed here. We uncover that not all of these extensions are fully-weighted;some depend on the degree and thus change a lot when an infinitely small weightedge is exchanged for the absence of an edge, a feature that is not alwaysdesirable. We call these methods ``hybrid'' and argue that, in many situations,one should prefer fully-weighted definitions. After listing the necessaryrequirements for a method to analyze many various weighted networks properly,we propose a fully-weighted continuous clustering coefficient that satisfiesall the previously proposed criteria while also being continuous with respectto vanishing weights. We demonstrate that the behavior and meaning of theZhang--Horvath clustering and our new continuous definition providecomplementary results and significantly outperform other definitions inmultiple relevant conditions. Using synthetic and real-world examples, we showthat when the network is inferred, noisy, or very heterogeneous, it isessential to use the fully-weighted clustering definitions.

Weighted directed clustering: interpretations and requirements for heterogeneous, inferred, and measured networks