scholarly journals A Strong Zero-One Law for Connectivity in One-Dimensional Geometric Random Graphs With Non-Vanishing Densities

2007 ◽  
Author(s):  
Guang Han ◽  
Armand M. Makowski
Keyword(s):  
Random Graphs ◽  
One Dimensional ◽  
Geometric Random Graphs

scholarly journals On Vertex, Edge, and Vertex-Edge Random Graphs

10.37236/597 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Elizabeth Beer ◽  
James Allen Fill ◽  
Svante Janson ◽  
Edward R. Scheinerman
Keyword(s):  
Random Graphs ◽  
Geometric Random Graphs

We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erdős-Rényi random graphs, vertex random graphs are generalizations of geometric random graphs, and vertex-edge random graphs generalize both. The names of these three types of random graphs describe where the randomness in the models lies: in the edges, in the vertices, or in both. We show that vertex-edge random graphs, ostensibly the most general of the three models, can be approximated arbitrarily closely by vertex random graphs, but that the two categories are distinct.

Point-based polygonal models for random graphs

1993 ◽  
Vol 25 (2) ◽  
pp. 348-372 ◽  
Author(s):  
T. Arak ◽  
P. Clifford ◽  
D. Surgailis
Keyword(s):  
Computer Simulations ◽  
Random Graphs ◽  
Particle System ◽  
Two Dimensional ◽  
One Dimensional ◽  
Space And Time ◽  
Markov Random ◽  
Alternative Description ◽  
Polygonal Models ◽  
Birth Death

We define a class of two-dimensional Markov random graphs with I, V, T and Y-shaped nodes (vertices). These are termed polygonal models. The construction extends our earlier work [1]– [5]. Most of the paper is concerned with consistent polygonal models which are both stationary and isotropic and which admit an alternative description in terms of the trajectories in space and time of a one-dimensional particle system with motion, birth, death and branching. Examples of computer simulations based on this description are given.

scholarly journals SPIN-MODELS OF GRANULAR COMPACTION: FROM ONE-DIMENSIONAL MODELS TO RANDOM GRAPHS

2001 ◽  
Vol 04 (04) ◽  
pp. 309-319 ◽  
Author(s):  
JOHANNES BERG ◽  
ANITA MEHTA
Keyword(s):  
Random Graphs ◽  
Granular Matter ◽  
Spin Hamiltonian ◽  
Spin Models ◽  
One Dimensional ◽  
Granular Assembly ◽  
Geometric Frustration ◽  
Granular Compaction ◽  
Dimensional Models

We discuss two athermal types of dynamics suitable for spin-models designed to model repeated tapping of a granular assembly. These dynamics are applied to a range of models characterized by a 3-spin Hamiltonian aiming to capture the geometric frustration in packings of granular matter.

Point-based polygonal models for random graphs

1993 ◽  
Vol 25 (02) ◽  
pp. 348-372 ◽  
Author(s):  
T. Arak ◽  
P. Clifford ◽  
D. Surgailis
Keyword(s):  
Computer Simulations ◽  
Random Graphs ◽  
Particle System ◽  
Two Dimensional ◽  
One Dimensional ◽  
Space And Time ◽  
Markov Random ◽  
Alternative Description ◽  
Polygonal Models ◽  
Birth Death

We define a class of two-dimensional Markov random graphs with I, V, T and Y-shaped nodes (vertices). These are termed polygonal models. The construction extends our earlier work [1]– [5]. Most of the paper is concerned with consistent polygonal models which are both stationary and isotropic and which admit an alternative description in terms of the trajectories in space and time of a one-dimensional particle system with motion, birth, death and branching. Examples of computer simulations based on this description are given.

scholarly journals Geometric random graphs and Rado sets in sequence spaces

2019 ◽  
Vol 79 ◽  
pp. 1-14
Author(s):  
Anthony Bonato ◽  
Jeannette Janssen ◽  
Anthony Quas
Keyword(s):  
Random Graphs ◽  
Sequence Spaces ◽  
Geometric Random Graphs
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