Inhomogenous Poisson Networks and Random Cellular Structures

we study the statistical properties of inhomogenous Poisson networks. we perform a detailed analysis of the statistical properties of Poisson networks and show that the topological properties of random cellular structures, can be derived from these models of random networks. we study both two and three dimensional networks with non uniform density and show that with a class of symmetric distribution $P({\lambda }_1,{\lambda }_2,\mathrm{.}\mathrm{.}\mathrm{.},{\lambda }_N)$ Lewis and Aboav-Weaire laws are obeyed in these networks.