As the nature and types of graphs in numerous fields such as social sciences, engineering, and biology continue to proliferate, common graph techniques no longer always suffice. In particular, we tackle the problem of visualizing dynamic weighted graphs—graphs with edges whose weight changes over time—to extract connectivity and sequencing patterns. We present LinkWave, a novel technique employing the concept of a visual list of edges. To better support the visual exploration of weight changes in edges and to characterize their rhythmic patterns, LinkWave represents each edge as an individual time series and provides a set of interactions to zoom, filter, sort, and aggregate the edges. We designed LinkWave in collaboration with neuroscientists seeking to extract patterns caused by degenerative diseases in functional brain connectivity data. We report preliminary findings neuroscientists discovered with LinkWave.