Intersection information in urban transportation networks is critical to the safe and efficient operation of road traffic. The controllability of the road network can be increased by controlling critical intersections during peak traffic periods. On the one hand, based on the improved intra- and inter-level correlation description matrix of time steps, a directed supra-adjacency matrix (DSAM) temporal network model is built to verify the validity of the model using the road network data of urban core areas and compare the results with those obtained from static critical intersection identification. The results show that the DSAM model has a phase continuity feature in ranking the intersection importance, which has richer connotation than the critical intersection identification results based on a single indicator and has better consistency at different time granularity. On the other hand, based on the DSAM model to identify critical intersections of road network, short-term traffic flow prediction is performed with the help of a road network adjacency matrix, and the results show that the Chebyshev diagram convolution neural network (ChebNet) has the best performance. It can be used in the detection of recurrent congestion of urban road networks, and corresponding control measures are made in shorter time steps, which can prevent the possibility of widespread congestion and reduce the blockage of the whole road network. In summary, the model can be used for critical intersection identification and congestion detection in urban road networks.