Fig. 5: Illustration of the method used to construct and compare transition matrices.

We present a schematic workflow summarising the steps involved in constructing and comparing the transition matrices, complementing the explanation provided in the corresponding section of the Methods. To simplify the exposition, we show a toy example with three snapshots of a directed network with fixed composition, where links take binary values (0 or 1). For each pair of consecutive snapshots, a transition matrix M^K is built based on the observed transitions across all edges, with each M^K constructed from N^K transitions. These transitions are then pooled to form a mixed set, from which an average transition matrix 〈m^K〉 is computed. The central question is whether each individual matrix M^K could be interpreted as a random resampling of the average matrix. To assess this, we generate 1000 surrogate matrices from the mixed pool and compare them element by element to compute null distances. The actual distance between M^K and its corresponding average is then evaluated against this null distribution to assess statistical compatibility.