  Structural properties of evolving random graphs are investigated. Treating
linking as a dynamic aggregation process, rate equations for the distribution
of node to node distances (paths) and of cycles are formulated and solved
analytically. At the gelation point, the typical length of paths and cycles, l,
scales with the component size k as l ~ k^{1/2}. Dynamic and finite-size
scaling laws for the behavior at and near the gelation point are obtained.
Finite-size scaling laws are verified using numerical simulations.
