Emergence of Long-Range Correlations in Random Networks
arXiv:2006.08132 · doi:10.1088/2632-072X/abb4c5
Abstract
We perform an analytical analysis of the long-range degree correlation of the giant component in an uncorrelated random network by employing generating functions. By introducing a characteristic length, we find that a pair of nodes in the giant component is negatively degree-correlated within the characteristic length and uncorrelated otherwise. At the critical point, where the giant component becomes fractal, the characteristic length diverges and the negative long-range degree correlation emerges. We further propose a correlation function for degrees of the -distant node pairs, which behaves as an exponentially decreasing function of distance in the off-critical region. The correlation function obeys a power-law with an exponential cutoff near the critical point. The Erdős-Rényi random graph is employed to confirm this critical behavior.
arXiv comment9 pages, 2 figures
References in corpus (28)
- Community detection in graphs
- Uncovering the overlapping community structure of complex networks in nature and society
- Defining and identifying communities in networks
- Hierarchical Organization in Complex Networks
- Self-similarity of complex networks
- Scale-Free Networks are Ultrasmall
- Origins of fractality in the growth of complex networks
- The topological relationship between the large-scale attributes and local interaction patterns of complex networks
- Construction and properties of assortative random networks
- Skeleton and fractal scaling in complex networks
- Scaling theory of transport in complex networks
- Quantifying randomness in real networks
- Small world-Fractal Transition in Complex Networks: Renormalization Group Approach
- Tuning clustering in random networks with arbitrary degree distributions
- Motif-based communities in complex networks
- Self-similar Scale-free Networks and Disassortativity
- Scaling of degree correlations and the influence on diffusion in scale-free networks
- Correlations in connected random graphs
- Disassortativity of percolating clusters in random networks
- Revealing the Micro-Structure of the Giant Component in Random Graph Ensembles
- General expression for the component size distribution in infinite configuration networks
- Clustering Spectrum of scale-free networks
- Quantifying long-range correlations in complex networks beyond nearest neighbors
- Fractality and degree correlations in scale-free networks
- A general formulation of long-range degree correlations in complex networks
- Structure of percolating clusters in random clustered networks
- Identification of intrinsic long-range degree correlations in complex networks
- Long-range disassortative correlations in generic random trees