  In this paper, we provide novel definitions of clustering coefficient for
weighted and directed multilayer networks. We extend in the multilayer
theoretical context the clustering coefficients proposed in the literature for
weighted directed monoplex networks. We quantify how deeply a node is involved
in a choesive structure focusing on a single node, on a single layer or on the
entire system. The coefficients convey several characteristics inherent to the
complex topology of the multilayer network. We test their effectiveness
applying them to a particularly complex structure such as the international
trade network. The trade data integrate different aspects and they can be
described by a directed and weighted multilayer network, where each layer
represents import and export relationships between countries for a given
sector. The proposed coefficients find successful application in describing the
interrelations of the trade network, allowing to disentangle the effects of
countries and sectors and jointly consider the interactions between them.
