Degree distribution of random Apollonian network structures and Boltzmann sampling
Abstrak
Random Apollonian networks have been recently introduced for representing real graphs. In this paper we study a modified version: random Apollonian network structures (RANS), which preserve the interesting properties of real graphs and can be handled with powerful tools of random generation. We exhibit a bijection between RANS and ternary trees, that transforms the degree of nodes in a RANS into the size of particular subtrees. The distribution of degrees in RANS can thus be analysed within a bivariate Boltzmann model for the generation of random trees, and we show that it has a Catalan form which reduces to a power law with an exponential cutoff: $α ^k k^{-3/2}$, with $α = 8/9$. We also show analogous distributions for the degree in RANS of higher dimension, related to trees of higher arity.
Topik & Kata Kunci
Penulis (2)
Alexis Darrasse
Michèle Soria
Akses Cepat
- Tahun Terbit
- 2007
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.3521
- Akses
- Open Access ✓