Before revision:  First, we examine the spectral gaps of tie-decay networks from empirical data .
After revision:  First, we examine the spectral gaps of tie-decay networks from empirical data with those for corresponding randomized and aggregate networks. We find that the spectral gaps of the empirical networks tend to be smaller than those of the randomized and aggregate networks. Second, we study the spectral gap as a function of the tie-decay rate and time.