Abstract
We study the average nearest-neighbour degree a(k) of vertices with degree k. In many real-world networks with power-law degree distribution, a(k) falls off with k, a property ascribed to the constraint that any two vertices are connected by at most one edge. We show that a(k) indeed decays with k in three simple random graph models with power-law degrees: the erased configuration model, the rank-1 inhomogeneous random graph, and the hyperbolic random graph. We find that in the large-network limit for all three null models, a(k) starts to decay beyond and then settles on a power law , with the degree exponent.
Original language | English |
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Pages (from-to) | 672-700 |
Number of pages | 29 |
Journal | Journal of applied probability |
Volume | 56 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Sep 2019 |
Externally published | Yes |
Keywords
- Degree correlations
- random graph