A visualization engine is configured to generate a network visualization that represents the evolution of a network over time. The visualization engine generates the network visualization based on a network dataset that describes various nodes within the network, and links between those nodes, over a sequence of time intervals. Initially, the visualization engine generates a stable simulated network based on initial network data, and then subsequently animates changes to that simulated network that derive from differences between the initial network data and subsequent network data. The visualization engine visually indicates changes to different nodes in the network via color changes, size changes, and other changes to the appearance of nodes.