Metric properties of fractal lattices

The authors study the connectivity dimension d of fractal lattices viewed as networks (graphs) of sites and (constant length) bond. Two examples are investigated in detail: the 2D Sierpinski gasket and 2D infinite percolation clusters on square and triangular lattices. In the first case d is shown to coincide with the fractal dimension, whereas d=1.72+or-0.02 appears as a universal exponent for percolation clusters in two dimensions. Considered as an intrinsic parameter, the connectivity dimension d is compared with other intrinsic and extrinsic characteristic parameters of fractal lattices. In particular the authors argue that d<or=d<or=d holds on fractal lattices in general (d=fractal dimension, d=spectral dimension).