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Complex networks evolve and vary their structure as time goes by. Inparticular, the links in those networks have both a sign and a directionality.To understand their structural principles, we measure the network motifs, whichare patterns that appear much more than one would expect in randomizednetworks, considering both link properties. We propose motif dynamics, which isa study to investigate the change in the number of motifs, and applied themotif dynamics to an open evolving network model and empirical data. We confirmthat a non-cyclic motif has a greater correlation with the system size than acyclic structural motif. Furthermore, the motif dynamics can give us insightinto the friendship between freshmen in a university.

Motif Dynamics in Signed Directional Complex Networks