### Abstract

Random nearest neighbor and influence graphs with vertex set Z^{d} are defined and their percolation properties are studied. The nearest neighbor graph has (with probability 1) only finite connected components and a superexponentially decaying connectivity function. Influence graphs (which are related to energy minimization searches in disordered Ising models) have a percolation transition.

Original language | English (US) |
---|---|

Pages (from-to) | 262-278 |

Number of pages | 17 |

Journal | Random Structures and Algorithms |

Volume | 15 |

Issue number | 3-4 |

State | Published - Oct 1999 |

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### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Mathematics(all)
- Applied Mathematics

### Cite this

*Random Structures and Algorithms*,

*15*(3-4), 262-278.

**Random nearest neighbor and influence graphs on Zd
.** / Nanda, S.; Newman, Charles.

Research output: Contribution to journal › Article

*Random Structures and Algorithms*, vol. 15, no. 3-4, pp. 262-278.

}

TY - JOUR

T1 - Random nearest neighbor and influence graphs on Zd

AU - Nanda, S.

AU - Newman, Charles

PY - 1999/10

Y1 - 1999/10

N2 - Random nearest neighbor and influence graphs with vertex set Zd are defined and their percolation properties are studied. The nearest neighbor graph has (with probability 1) only finite connected components and a superexponentially decaying connectivity function. Influence graphs (which are related to energy minimization searches in disordered Ising models) have a percolation transition.

AB - Random nearest neighbor and influence graphs with vertex set Zd are defined and their percolation properties are studied. The nearest neighbor graph has (with probability 1) only finite connected components and a superexponentially decaying connectivity function. Influence graphs (which are related to energy minimization searches in disordered Ising models) have a percolation transition.

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UR - http://www.scopus.com/inward/citedby.url?scp=0033441959&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033441959

VL - 15

SP - 262

EP - 278

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 3-4

ER -