Organization of complex networks without multiple connections

Abstract

We find a new structural feature of equilibrium complex random networks without multiple and self-connections. We show that if the number of connections is sufficiently high, these networks contain a core of highly interconnected vertices. The number of vertices in this core varies in the range between $const{N}^{1/2}$ and $const{N}^{2/3}$, where $N$ is the number of vertices in a network. At the birth point of the core, we obtain the size-dependent cut-off of the distribution of the number of connections and find that its position differs from earlier estimates.

5 pages, 2 figures

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• Finite size effects in Barabasi-Albert growing networks
• Dynamics of condensation in growing complex networks
• Condensation and topological phase transitions in a dynamical network model with rewiring of the links
• Condensation of degrees emerging through a first-order phase transition in classical random graphs
• Approaching the thermodynamic limit in equilibrated scale-free networks
• Condensation phase transition in nonlinear fitness networks
• Tsallis mapping in growing complex networks with fitness
• Phase transitions in atypical systems induced by a condensation transition on graphs