Feeding relationships can cause invasions, extirpations, and population fluctuations of a species to dramatically affect other species within a variety of natural habitats. Empirical evidence suggests that such strong effects rarely propagate through food webs more than three links away from the initial perturbation.

We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of the Laplacian of the graph. We show numerically that the addition of random shortcuts produces improved network synchronizability.

Two interesting points: 1. The seed set for AltaVista must be at least 10 million (actually, presumably, much larger). Creating a huge seed set almost as important as crawling.2. How on earth does AltaVista find URLs for 10 million isolated pages?