Formation of Modularity in a Model of Evolving Networks

Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the observations of real social networks, we introduced a link-creating/deleting strategy according to the local dynamics in the model. Thus the coevolution of dynamics and topology naturally determines the network properties. It is found that for a small coupling strength, the networked system cannot reach any synchronization and the network topology is homogeneous. Interestingly, when the coupling strength is large enough, the networked system spontaneously forms communities with different dynamical states. Meanwhile, the network topology becomes heterogeneous with modular structures. It is further shown that in a certain parameter regime, both the degree and the community size in the formed network follow a power-law distribution, and the networks are found to be assortative. These results are consistent with the characteristics of many empirical networks, and are helpful to understand the mechanism of formation of modularity in complex networks.Comment: 6 pages, 4 figur

Growth, collapse, and self-organized criticality in complex networks

abstract: Network growth is ubiquitous in nature (e.g., biological networks) and technological systems (e.g., modern infrastructures). To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the question of whether a complex network of nonlinear oscillators can maintain its synchronization stability as it expands. We find that a large scale avalanche over the entire network can be triggered in the sense that the individual nodal dynamics diverges from the synchronous state in a cascading manner within a relatively short time period. In particular, after an initial stage of linear growth, the network typically evolves into a critical state where the addition of a single new node can cause a group of nodes to lose synchronization, leading to synchronization collapse for the entire network. A statistical analysis reveals that the collapse size is approximately algebraically distributed, indicating the emergence of self-organized criticality. We demonstrate the generality of the phenomenon of synchronization collapse using a variety of complex network models, and uncover the underlying dynamical mechanism through an eigenvector analysis.The final version of this article, as published in Scientific Reports, can be viewed online at: https://www.nature.com/articles/srep2444