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We uncover the global organization of clustering in real complex networks. Asit happens with other fundamental properties of networks such as the degreedistribution, we find that real networks are neither completely random norordered with respect to clustering, although they tend to be closer tomaximally random architectures. We reach this conclusion by comparing theglobal structure of clustering in real networks with that in maximally randomand in maximally ordered clustered graphs. The former are produced with anexponential random graph model that maintains correlations among adjacent edgesat the minimum needed to conform with the expected clustering spectrum; thelater with a random model that arranges triangles in cliques inducing highlyordered structures. To compare the global organization of clustering in realand model networks, we compute $m$-core landscapes, where the $m$-core isdefined, akin to the $k$-core, as the maximal subgraph with edges participatingat least in $m$ triangles. This property defines a set of nested subgraphsthat, contrarily to $k$-cores, is able to distinguish between hierarchical andmodular architectures. To visualize the $m$-core decomposition we developed theLaNet-vi 3.0 tool.

Deciphering the global organization of clustering in real complex networks