A new deterministic complex network model with hierarchical structure

Abstract

We introduce a new simple pseudo tree-like network model, deterministic complex network (DCN). The proposed DCN model may simulate the hierarchical structure nature of real networks appropriately and have the unique property of ‘skipping the levels’, which is ubiquitous in social networks. Our results indicate that the DCN model has a rather small average path length and large clustering coefficient, leading to the small-world effect. Strikingly, our DCN model obeys a discrete power-law degree distribution P( k)∝ k − γ , with exponent γ approaching 1.0. We also discover that the relationship between the clustering coefficient and degree follows the scaling law C( k)∼ k −1, which quantitatively determines the DCN's hierarchical structure.