Social Climber attachment in forming networks produces phase transition in a measure of connectivity

Abstract

Formation and fragmentation of networks is typically studied using percolation theory, but most previous research has been restricted to studying a phase transition in cluster size, examining the emergence of a giant component. This approach does not study the effects of evolving network structure on dynamics that occur at the nodes, such as the synchronization of oscillators and the spread of information, epidemics, and neuronal excitations. We introduce and analyze new link-formation rules, called Social Climber (SC) attachment, that may be combined with arbitrary percolation models to produce a previously unstudied phase transition using the largest eigenvalue of the network adjacency matrix as the order parameter. This eigenvalue is significant in the analyses of many network-coupled dynamical systems in which it measures the quality of global coupling and is hence a natural measure of connectivity. We highlight the important self-organized properties of SC attachment and discuss implications for controlling dynamics on networks.

6 pages, 4 figures

References in corpus (13)

• Efficient Immunization Strategies for Computer Networks and Populations
• Cascade control and defense in complex networks
• Understanding the spreading patterns of mobile phone viruses
• Characterizing the dynamical importance of network nodes and links
• Explosive percolation in scale-free networks
• Explosive percolation via control of the largest cluster
• Approximating the largest eigenvalue of network adjacency matrices
• Statistical Properties of Avalanches in Networks
• Weighted percolation on directed networks
• Modular networks emerge from multiconstraint optimization
• Dynamical Instability in Boolean Networks as a Percolation Problem
• Spectral Perturbation and Reconstructability of Complex Networks
• A network-specific approach to percolation in networks with bidirectional links

Cited by in corpus (5)

• Nestedness in complex networks: Observation, emergence, and implications
• Synchronization of heterogeneous oscillators under network modifications: Perturbation and optimization of the synchrony alignment function
• The Social Climbing Game
• Spectral Anlysis on Explosive Percolation
• Spectral properties of the hierarchical product of graphs