  Network science investigates the architecture of complex systems to
understand their functional and dynamical properties. Structural patterns such
as communities shape diffusive processes on networks. However, these results
hold under the strong assumption that networks are static entities where
temporal aspects can be neglected. Here we propose a generalised formalism for
linear dynamics on complex networks, able to incorporate statistical properties
of the timings at which events occur. We show that the diffusion dynamics is
affected by the network community structure and by the temporal properties of
waiting times between events. We identify the main mechanism --- network
structure, burstiness or fat-tails of waiting times --- determining the
relaxation times of stochastic processes on temporal networks, in the absence
of temporal-structure correlations. We identify situations when fine-scale
structure can be discarded from the description of the dynamics or, conversely,
when a fully detailed model is required due to temporal heterogeneities.
