  We present a novel method for analysing socio-spatial segregation in cities
by considering constraints imposed by transportation networks. Using a
multilayered network approach, we model the interaction probabilities of
socio-economic groups with random walks and L\'evy flights. This method allows
for evaluation of new transport infrastructure's impact on segregation while
quantifying each network's contribution to interaction opportunities. The
proposed random walk segregation index measures the probability of individuals
encountering diverse social groups based on their available means of transit
via random walks. The index incorporates temporal constraints in urban mobility
with a parameter, $\alpha \in [0,1)$, of the probability of the random walk
continuing at each time step. By applying this to a toy model and conducting a
sensitivity analysis, we explore how the index changes dependent on this
temporal constraint. When the parameter equals zero, the measure simplifies to
an isolation index. When the parameter approaches one it represents the city's
overall socio-economic distribution by mirroring the steady-state of the random
walk process. Using Cuenca, Ecuador as a case study, we illustrate the method's
applicability in transportation planning as a valuable tool for policymakers,
addressing spatial distribution of socio-economic groups and the connectivity
of existing transport networks, thus promoting equitable interactions
throughout the city.
