  Geometry of networks endowed with a causal structure is discussed using the
conventional framework of equilibrium statistical mechanics. The popular
growing network models appear as particular causal models. We focus on a class
of tree graphs, an analytically solvable case. General formulae are derived,
describing the degree distribution, the ancestor-descendant correlation and the
probability a randomly chosen node lives at a given geodesic distance from the
root. It is shown that the Hausdorff dimension $d_H$ of the causal networks is
generically infinite, in contrast to the maximally random trees, where it is
generically finite.
