# On the mixing time of geographical threshold graphs

## Abstract

In this paper, we study the mixing time of random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). We specifically study the mixing times of random walks on 2-dimensional GTGs near the connectivity threshold. We provide a set of criteria on the distribution of vertex weights that guarantees that the mixing time is {Theta}(n log n).

- Authors:

- Los Alamos National Laboratory

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 988314

- Report Number(s):
- LA-UR-09-02151; LA-UR-09-2151

TRN: US201018%%480

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Conference

- Resource Relation:
- Conference: Random Approx '01 Meeting ; August 21, 2009 ; Berkeley, CA, USA

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97; DISTRIBUTION; EUCLIDEAN SPACE; INTERNET

### Citation Formats

```
Bradonjic, Milan.
```*On the mixing time of geographical threshold graphs*. United States: N. p., 2009.
Web.

```
Bradonjic, Milan.
```*On the mixing time of geographical threshold graphs*. United States.

```
Bradonjic, Milan. Thu .
"On the mixing time of geographical threshold graphs". United States. https://www.osti.gov/servlets/purl/988314.
```

```
@article{osti_988314,
```

title = {On the mixing time of geographical threshold graphs},

author = {Bradonjic, Milan},

abstractNote = {In this paper, we study the mixing time of random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). We specifically study the mixing times of random walks on 2-dimensional GTGs near the connectivity threshold. We provide a set of criteria on the distribution of vertex weights that guarantees that the mixing time is {Theta}(n log n).},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2009},

month = {1}

}