  A number of network structural characteristics have recently been the subject
of particularly intense research, including degree distributions, community
structure, and various measures of vertex centrality, to mention only a few.
Vertices may have attributes associated with them; for example, properties of
proteins in protein-protein interaction networks, users' social network
profiles, or authors' publication histories in co-authorship networks. In a
network, two vertices might be considered similar if they have similar
attributes (features, properties), or they can be considered similar based
solely on the network structure. Similarity of this type is called structural
similarity, to distinguish it from properties similarity, social similarity,
textual similarity, functional similarity or other similarity types found in
networks. Here we focus on the similarity problem by computing (1) for each
vertex a vector of structural features, called signature vector, based on the
number of graphlets associated with the vertex, and (2) for the network its
graphlet correlation matrix, measuring graphlets dependencies and hence
revealing unknown organizational principles of the network. We found that
real-world networks generally have very different structural characteristics
resulting in different graphlet correlation matrices. In particular, the
graphlet correlation matrix of the brain effective network is computed for 40
healthy subjects and common (present in more than 70 percent subjects)
dependencies are raveled. Thus, negative correlations are found for 2-node
graphlets and 3-node graphlets that are wedges and positive correlations are
found only for 3-node graphlets that are triangles. Graphlets characteristics
in directed networks could further significantly increase our understanding of
real-world networks.
