The energy landscape approach has been useful to help understand the dynamic properties of supercooled liquids and the connection between these properties and thermodynamics. The analysis in numerical models of the inherent structure (IS) trajectories-the set of local minima visited by the liquid-offers the possibility of filtering out the vibrational component of the motion of the system on the potential energy surface and thereby resolving the slow structural component more efficiently. Here we report an analysis of an IS trajectory for a widely studied water model, focusing on the changes in hydrogen bond connectivity that give rise to many IS's separated by relatively small energy barriers. We find that while the system travels through these IS's, the structure of the bond network is continuously modified, exchanging linear bonds for bifurcated bonds and usually reversing the exchange to return to nearly the same initial configuration. For the 216-molecule system we investigate, the time scale of these transitions is as small as the simulation time scale ( approximately 1 fs). Hence, for water, the transition between each of these IS's is relatively small and eventual relaxation of the system occurs only by many of these transitions. We find that during IS changes the molecules with the greatest displacements move in small "clusters" of 1-10 molecules with displacements of approximately 0.02-0.2 nm, not unlike simpler liquids. However, for water these clusters appear to be somewhat more branched than the linear "stringlike" clusters formed in a supercooled Lennard-Jones system found by Glotzer and her collaborators.