  Weights and directionality of the edges carry a large part of the information
we can extract from a complex network. However, many network measures were
formulated initially for undirected binary networks. The necessity to
incorporate information about the weights led to the conception of the multiple
extensions, particularly for definitions of the local clustering coefficient
discussed 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 weight
edge is exchanged for the absence of an edge, a feature that is not always
desirable. We call these methods ``hybrid'' and argue that, in many situations,
one should prefer fully-weighted definitions. After listing the necessary
requirements for a method to analyze many various weighted networks properly,
we propose a fully-weighted continuous clustering coefficient that satisfies
all the previously proposed criteria while also being continuous with respect
to vanishing weights. We demonstrate that the behavior and meaning of the
Zhang--Horvath clustering and our new continuous definition provide
complementary results and significantly outperform other definitions in
multiple relevant conditions. Using synthetic and real-world examples, we show
that when the network is inferred, noisy, or very heterogeneous, it is
essential to use the fully-weighted clustering definitions.
