POINT-BASED POLYGONAL MODELS FOR RANDOM GRAPHS

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 c oncerned with consistent polygonal models which are both stationary an d isotropic and which admit an alternative description in terms of the trajectories in space and time of a one-dimensional particle system w ith motion, birth, death and branching. Examples of computer simulatio ns based on this description are given.