The arrangement of cells in 3- and 4-regular planar networks formed by random straight lines
M. Amaral Fortes, P. N. Andrade · Journal de physique · 1989
The relation between mi, the average number of sides in cells adjacent to i-sided cells, and i, was investigated in planar networks of two types, generated by random, Poisson distributed, straight lines. When the lines are continuous, a 4-regular network results. If the lines are interrupted to form T-junctions, a 3-regular network is obtained. In the first case, two types of cell adjacency can be defined and for both mi varies approximately linearly with 1/i. The same applies to the 3-regular network. The linear relations (Aboav's law) can be put in a general form, involving the second moment of the distribution of cell polygonalities and a single parameter, a, as suggested by Weaire.