Tortuosity of Delaunay Triangulations and Statistics of Shortest Paths

A tortuosity τDln of the Delaunay triangulation on plane and in 3D-space is defined and numerically calculated. This coefficient appears naturally in the porous media studies. The conjecture on the average number of links in the shortest path between two arbitrary points is formulated and statistically studied. The distribution of the number of links in the shortest paths in triangulations of square and disc on R2 is described.