(color online) (a) An example of a random network with N = 100 nodes, and each node connects to other nodes with the same degree k = 3. (b), (c) The spatiotemporal evolution patterns of two different oscillatory states in the same network shown in panel (a) by starting from different initial conditions. Both patterns display the evolution of local variable u. The nodes are spatially arranged according to their indices i. (d) The DPAD structure corresponding to the oscillation state in panel (b), where a loop and multiple chains are identified; (e) the DPAD structure corresponding to the oscillation state in panel (c), where two independent subgraphs are found with each subgraph containing a loop and numerous chains. (Adapted from Ref. [38]).