Inferring links in directed complex networks through feed forward loop motifs

Complex networks are mathematical abstractions of real-world systems using sets of nodes and edges representing the entities and their interactions. Prediction of unknown interactions in such networks is a problem of interest in biology, sociology, physics, engineering, etc. Most complex networks exhibit the recurrence of subnetworks, called network motifs. Within the realm of social science, link prediction (LP) models are employed to model opinions, trust, privacy, rumor spreading in social media, academic and corporate collaborations, liaisons among lawbreakers, and human mobility resulting in contagion. We present an LP metric based on a motif in directed complex networks, called feed-forward loop (FFL). Unlike nearest neighbor-based metrics and machine learning-based techniques that gauge the likelihood of a link based on node similarity, the proposed approach leverages a known dichotomy in the motif distribution of directed networks. Complex networks are sparse, causing most nodes and their associated links to have low motif participation. Yet, due to intrinsic network motif-richness, few links participate in many distinct motif substructures. Thus, the FFL-based metric combines the presence and absence of motifs as a signature to outperform baseline metrics on ten directed social and biological network datasets. We conclude with the future of the FFL-based metric in dynamic network inference as well as its use in designing combined metrics using network motifs of varying orders as features.