Abstract
In this paper we consider random distance graphs motivated by applications in neurobiology. These models can be viewed as examples of inhomogeneous random graphs, notably outside of the so-called rank-1 case. Treating these models in the context of the general theory of inhomogeneous graphs helps us to derive the asymptotics for the size of the largest connected component. In particular, we show that certain random distance graphs behave exactly as the classical Erdos-Rényi model, not only in the supercritical phase (as already known) but in the subcritical case as well.
| Original language | English |
|---|---|
| Journal | Journal of Applied Probability |
| Volume | 54 |
| Issue number | 4 |
| Pages (from-to) | 1278-1294 |
| Number of pages | 17 |
| ISSN | 0021-9002 |
| DOIs | |
| Publication status | Published - Dec 2017 |
| Externally published | Yes |
Keywords
- Inhomogeneous random graph
- largest connected component
- random distance graph