Graphlet characteristics in directed networks

Abstract

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.

Graphlet-based Characterization of Directed Networks

“…Research on uncovering their organizational principles and function will continue. Applying our new directed graphlet-based methods, or devising new methods for their analyses 62 63 are a subject of future research.…”

Inhibitory interaction networks among coevolved Streptomyces populations from prairie soils

“…Analyses of node participation within realized network substructures (graphlets) offers an alternative approach to identifying important organizational patterns within and among networks [26, 47, 48]. To compare the participation of each Streptomyces isolate (node) in three-member triads within each community, we quantified the participation of each node in three-member interactions while taking in to account the position of each node.…”

“…Isolates that hold similar positions are expected to play similar biological roles within their local communities. The frequency of node positions within each connected triad (for a total of 30 isomorphic node positions; Fig 2; [26] was used to generate a ‘signature vector’ for each node. The signature vector represents the cumulative local graph structure of each node (isolate).…”

“…As a result, triad censuses have been used to understand the tendency of networks to support social, hierarchical, or transitive relationships. Similarly, though motif analysis requires the use of null network models, analyses of observed network sub-structures can shed further light on the biology of complex systems [26]. Analysis of graphlets, or induced network substructures, is not dependent on null network models and offers unique insights into the roles that particular nodes play across distinct networks [26].…”

Dissecting molecular network structures using a network subgraph approach

“…Besides network motif description, Przulj (2007) and Yaveroğlu et al (2014) utilized a graphlet-based approach to examine the network comparison problem. Directed graphlets are superior for comparing directed networks ( Martin et al, 2017 ; Trpevski et al, 2016 ) and they are effective for studying brain networks ( Sarajlić et al, 2016 ). Our study focused on networks composed of regulatory interactions (directed graphs), such as gene regulation networks and signal transduction networks, but not protein–protein interaction networks (undirected graphs).…”