The problem of clustering transportation networks has been studied in the static framework by considering traffic conditions at a given time. Nevertheless, it is important to underline that traffic is a strongly time-variant process and it needs to be studied in the spatio-temporal dimension. Considering the fact that the congestion is spatially correlated in adjacent roads and it propagates with different speeds, partitioning a transport network into homogeneous trajectories that evolve over time can be extremely useful in order to design a real-time traffic control schema which alleviate or postpone congestion. The paper proposes an evolutionary spectral clustering approach to partition a graph transport network into connected homogeneous trajectories that evolve over time. In order to choose the number of clusters automatically, we use the density peaks algorithm which is based on the idea that cluster centers are characterized by a higher density than their neighbors and by relatively large distance from trajectories with higher densities. The clusters are recognized and the outliers are excluded from the analysis. This method is proved to be efficient regardless the shape and the dimension of the data set. We perform experiments on real road speeds for Amsterdam city traffic network, our results show that the proposed evolutionary spectral clustering algorithm outperforms the static clustering algorithms in its efficiency and robustness.