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We present a novel method for analysing socio-spatial segregation in citiesby considering constraints imposed by transportation networks. Using amultilayered network approach, we model the interaction probabilities ofsocio-economic groups with random walks and L\'evy flights. This method allowsfor evaluation of new transport infrastructure's impact on segregation whilequantifying each network's contribution to interaction opportunities. Theproposed random walk segregation index measures the probability of individualsencountering diverse social groups based on their available means of transitvia random walks. The index incorporates temporal constraints in urban mobilitywith a parameter, $\alpha \in [0,1)$, of the probability of the random walkcontinuing at each time step. By applying this to a toy model and conducting asensitivity analysis, we explore how the index changes dependent on thistemporal constraint. When the parameter equals zero, the measure simplifies toan isolation index. When the parameter approaches one it represents the city'soverall socio-economic distribution by mirroring the steady-state of the randomwalk process. Using Cuenca, Ecuador as a case study, we illustrate the method'sapplicability in transportation planning as a valuable tool for policymakers,addressing spatial distribution of socio-economic groups and the connectivityof existing transport networks, thus promoting equitable interactionsthroughout the city.

Urban Segregation on multilayered transport networks: a random walk approach