Fig. 4

Memory effects on network pathways. a, b A discrete random walk starting at Medicine 13 in the state networks of \({\mathcal {M}}_1\) and \({\mathcal {M}}_2\), modelled as a discrete time diffusion over the transition matrices \(P_1\) and \(P_2\) respectively. After a single discrete time step \(t=1\) the reachable number of wards is similar between \({\mathcal {M}}_1\) and \({\mathcal {M}}_2\), however, they quickly diverge as the diffusion evolves over time and the transitive effects increase in \({\mathcal {M}}_1\). c, d Median size of the reachable set of wards for \({\mathcal {M}}_1\) and \({\mathcal {M}}_2\): c Overall reachability after t-discrete steps, and d reachability after t-discrete steps broken down by speciality (in the largest connected component)