  We uncover the global organization of clustering in real complex networks. As
it happens with other fundamental properties of networks such as the degree
distribution, we find that real networks are neither completely random nor
ordered with respect to clustering, although they tend to be closer to
maximally random architectures. We reach this conclusion by comparing the
global structure of clustering in real networks with that in maximally random
and in maximally ordered clustered graphs. The former are produced with an
exponential random graph model that maintains correlations among adjacent edges
at the minimum needed to conform with the expected clustering spectrum; the
later with a random model that arranges triangles in cliques inducing highly
ordered structures. To compare the global organization of clustering in real
and model networks, we compute $m$-core landscapes, where the $m$-core is
defined, akin to the $k$-core, as the maximal subgraph with edges participating
at least in $m$ triangles. This property defines a set of nested subgraphs
that, contrarily to $k$-cores, is able to distinguish between hierarchical and
modular architectures. To visualize the $m$-core decomposition we developed the
LaNet-vi 3.0 tool.
