Interplay between structure and dynamics in adaptive complex networks: Emergence and amplification of modularity by adaptive dynamics

Many real networks display modular organization, which can influence dynamical clustering on the networks. Therefore, there have been proposals put forth recently to detect network communities by using dynamical clustering. In this paper, we study how the feedback from dynamical clusters can shape the network connection weights with a weight-adaptation scheme motivated from Hebbian learning in neural systems. We show that such a scheme generically leads to the formation of community structure in globally coupled chaotic oscillators. The number of communities in the adaptive network depends on coupling strength c and adaptation strength r. In a modular network, the adaptation scheme will enhance the intramodule connection weights and weaken the intermodule connection strengths, generating effectively separated dynamical clusters that coincide with the communities of the network. In this sense, the modularity of the network is amplified by the adaptation. Thus, for a network with a strong community structure, the adaptation scheme can evidently reflect its community structure by the resulting amplified weighted network. For a network with a weak community structure, the statistical properties of synchronization clusters from different realizations can be used to amplify the modularity of the communities so that they can be detected reliably by the other traditional algorithms.