title: Nonlinear growth: an origin of hub organization in complex networks.
abstract: Many real-world networks contain highly connected nodes called hubs. Hubs are often crucial for network function and spreading dynamics. However, classical models of how hubs originate during network development unrealistically assume that new nodes attain information about the connectivity (for example the degree) of existing nodes. Here, we introduce hub formation through nonlinear growth where the number of nodes generated at each stage increases over time and new nodes form connections independent of target node features. Our model reproduces variation in number of connections, hub occurrence time, and rich-club organization of networks ranging from protein-protein, neuronal and fibre tract brain networks to airline networks. Moreover, nonlinear growth gives a more generic representation of these networks compared with previous preferential attachment or duplication-divergence models. Overall, hub creation through nonlinear network expansion can serve as a benchmark model for studying the development of many real-world networks.
authors.affiliation: Institute of Neuroscience, Newcastle University, Newcastle upon Tyne NE2 4HH, UK; Interdisciplinary Computing and Complex BioSystems Research Group (ICOS), School of Computing Science, Newcastle University, Newcastle upon Tyne NE1 7RU, UK.
authors.forename: Roman
authors.identifier: 0000-0002-7268-9359
authors.initials: R
authors.lastname: Bauer
authors.affiliation: Institute of Neuroscience, Newcastle University, Newcastle upon Tyne NE2 4HH, UK; Interdisciplinary Computing and Complex BioSystems Research Group (ICOS), School of Computing Science, Newcastle University, Newcastle upon Tyne NE1 7RU, UK.
authors.forename: Marcus
authors.initials: M
authors.lastname: Kaiser
keywords: complex networks; hubs; neural development; nonlinear growth; physical space; rich-club organization