Graphlet characteristics in directed networks

Graphlet analysis is part of network theory that does not depend on the choice of the network null model and can provide comprehensive description of the local network structure. Here, we propose a novel method for graphlet-based analysis of directed networks by computing first the signature vector for every vertex in the network and then the graphlet correlation matrix of the network. This analysis has been applied to brain effective connectivity networks by considering both direction and sign (inhibitory or excitatory) of the underlying directed (effective) connectivity. In particular, the signature vectors for brain regions and the graphlet correlation matrices of the brain effective network are computed for 40 healthy subjects and common dependencies are revealed. We found that the signature vectors (node, wedge, and triangle degrees) are dominant for the excitatory effective brain networks. Moreover, by considering only those correlations (or anti correlations) in the correlation matrix that are significant (>0.7 or <-0.7) and are presented in more than 60% of the subjects, we found that excitatory effective brain networks show stronger causal (measured with Granger causality) patterns (G-causes and G-effects) than inhibitory effective brain networks.