  The study of the sub-structure of complex networks is of major importance to
relate topology and functionality. Many efforts have been devoted to the
analysis of the modular structure of networks using the quality function known
as modularity. However, generally speaking, the relation between topological
modules and functional groups is still unknown, and depends on the semantic of
the links. Sometimes, we know in advance that many connections are transitive
and, as a consequence, triangles have a specific meaning. Here we propose the
study of the modular structure of networks considering triangles as the
building blocks of modules. The method generalizes the standard modularity and
uses spectral optimization to find its maximum. We compare the partitions
obtained with those resulting from the optimization of the standard modularity
in several real networks. The results show that the information reported by the
analysis of modules of triangles complements the information of the classical
modularity analysis.
