Fig. 1: Illustration of temporal dissimilarity characterization.

a, b Visualization of two temporal networks G₁ and G₂, which share the same number of nodes N and window size T; c The aggregated static network of G₁ and G₂; d Temporal paths between nodes 1 and 2 in G₁. e−g Illustration of computing the dissimilarity between G₁ and G₂. Firstly, we compute the FAD matrix, i.e., the first arrival distance between node pairs, for G₁ and G₂, respectively. Here, we denote \({l}_{\max }(G)\) to be the maximal FAD among all first arrival paths in temporal network G. When a first arrive path does not exist between two nodes thus the two nodes are not reachable, the corresponding FAD is set as \({l}_{\max }(G)+1\). This happens in G₁, and we have \({l}_{\max }({G}_{1})=2\). Secondly, the FAD distribution H_i of node i and \({\mu }_{{G}_{1}}({\mu }_{{G}_{2}})\) of the whole network are computed according to the FAD matrix. Finally, the temporal node dispersion (TNND) and temporal dissimilarity (TD(G₁, G₂)) are given based on Eqs. (1) and (2).