  Studying the topology of so-called real networks, that is networks obtained
from sociological or biological data for instance, has become a major field of
interest in the last decade. One way to deal with it is to consider that
networks are built from small functional units called motifs, which can be
found by looking for small subgraphs whose numbers of occurrences in the whole
network are surprisingly high. In this article, we propose to define motifs
through a local overrepresentation in the network and develop a statistic to
detect them without relying on simulations. We then illustrate the performance
of our procedure on simulated and real data, recovering already known
biologically relevant motifs. Moreover, we explain how our method gives some
information about the respective roles of the vertices in a motif.
