title: Assortative and modular networks are shaped by adaptive synchronization processes.
abstract: Modular organization and degree-degree correlations are ubiquitous in the connectivity structure of biological, technological, and social interacting systems. So far most studies have concentrated on unveiling both features in real world networks, but a model that succeeds in generating them simultaneously is needed. We consider a network of interacting phase oscillators, and an adaptation mechanism for the coupling that promotes the connection strengths between those elements that are dynamically correlated. We show that, under these circumstances, the dynamical organization of the oscillators shapes the topology of the graph in such a way that modularity and assortativity features emerge spontaneously and simultaneously. In turn, we prove that such an emergent structure is associated with an asymptotic arrangement of the collective dynamical state of the network into cluster synchronization.
authors.affiliation: Postgraduate Division in Systems Engineering, Department of Mechanical and Electrical Engineering, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, Nuevo León, Mexico.
authors.forename: Vanesa
authors.initials: V
authors.lastname: Avalos-Gaytán
authors.forename: Juan A
authors.initials: JA
authors.lastname: Almendral
authors.forename: David
authors.initials: D
authors.lastname: Papo
authors.forename: Satu Elisa
authors.initials: SE
authors.lastname: Schaeffer
authors.forename: Stefano
authors.initials: S
authors.lastname: Boccaletti
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D008962:Models, Theoretical; D009991:Oscillometry / Q000379:methods*