From mobility traces to process networks: evidence of structural heterogeneity in the Lisbon Metropolitan Area

Abstract
Typically, past works on urban mobility have leveraged origin–destination analysis to capture where people travel, often leaving the sequence and structure of their trips unaddressed, thereby limiting the diagnosis of accessibility inequalities. We address this gap by integrating process mining and network science, applying both frameworks to Call Detail Records (CDRs) from the Lisbon Metropolitan Area. From 2.7 million reconstructed trips, we construct case-centric event logs and discover Directly-Follows Graphs (DFGs) for morning commuting in each of the 18 municipalities. We represent these DFGs as weighted directed networks and compare them using eight complementary metrics, including degree-distribution Wasserstein distance, flow correlation, Jensen–Shannon divergence, and a composite complexity index. This reveals systematic structural heterogeneity that aggregated OD analysis cannot detect. Lisbon city emerges as a structural outlier, with the highest modal diversity and most complex DFG topology, whereas most peripheral municipalities are dominated by private car use. Geographic proximity does not guarantee temporal accessibility: median commutes between neighbouring municipalities such as Sintra and Cascais exceed 25 min, indicating infrastructure gaps. Municipalities cluster into spatially coherent groups defined by shared mobility process structures−a northern suburban cluster, a southern Tagus cluster, and an outlying Lisbon cluster−patterns that are consistent across structural and temporal metrics. Inferred commuting patterns align strongly with 2021 Census data (Pearson r = 0.94, Spearman ρ = 0.90), supporting the validity of the approach. We show that process mining and network science are complementary: process mining yields structured event representations and modal sequencing, while network science offers robust tools for structural comparison. However, DFG structures represent only mode–destination transitions, not full multimodal trip chains, a limitation to be addressed in future works.
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Funding
The authors acknowledge the financial support provided by FCT Portugal under the project UIDB/04152/2020 – Centro de Investigação em Gestão de Informação (MagIC/NovaIMS) (https://doi.org/10.54499/UIDB/04152/2020 and Project Enhance - F-DUT-2022-0393.
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Filonchik, K., Pinto, J.D., Pinheiro, F.L. et al. From mobility traces to process networks: evidence of structural heterogeneity in the Lisbon Metropolitan Area. Appl Netw Sci (2026). https://doi.org/10.1007/s41109-026-00822-2
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DOI: https://doi.org/10.1007/s41109-026-00822-2

Facts Only

* The study used Call Detail Records (CDRs) from the Lisbon Metropolitan Area.
* 2.7 million reconstructed trips were analyzed to construct case-centric event logs and Directly-Follows Graphs (DFGs) for morning commuting in 18 municipalities.
* DFGs were represented as weighted directed networks, compared using eight metrics, including degree-distribution Wasserstein distance, flow correlation, Jensen–Shannon divergence, and a composite complexity index.
* Lisbon city was identified as a structural outlier with the highest modal diversity and most complex DFG topology.
* Most peripheral municipalities are dominated by private car use.
* Median commutes between neighboring municipalities like Sintra and Cascais exceed 25 minutes.
* Municipalities cluster into spatially coherent groups defined by shared mobility process structures (northern suburban, southern Tagus, Lisbon outlier).
* Inferred commuting patterns showed a strong correlation with 2021 Census data (Pearson r = 0.94, Spearman $\rho$ = 0.90).
* Process mining provides structured event representations and modal sequencing; network science provides structural comparison tools.

Executive Summary

Origin-destination analysis alone is insufficient for diagnosing accessibility inequalities in urban mobility because it fails to capture the sequence and structure of trips. The research integrates process mining and network science, applying both frameworks to Call Detail Records (CDRs) from the Lisbon Metropolitan Area. From 2.7 million reconstructed trips, case-centric event logs and Directly-Follows Graphs (DFGs) were constructed for morning commuting across 18 municipalities. These DFGs were analyzed using eight metrics, including degree-distribution Wasserstein distance and Jensen–Shannon divergence, revealing structural heterogeneity not visible through aggregated OD analysis. The study identified Lisbon as a structural outlier with the highest modal diversity and most complex DFG topology, while peripheral municipalities show dominance by private car use. Furthermore, geographic proximity does not correlate with temporal accessibility, as median commutes between neighbors like Sintra and Cascais exceed 25 minutes, indicating infrastructure deficits. Municipalities cluster into coherent groups defined by shared mobility process structures, such as a northern suburban cluster and a southern Tagus cluster. These inferred commuting patterns align strongly with 2021 Census data.

Full Take

The integration of process mining and network science successfully moves beyond simple origin-destination metrics to map the underlying *process* of mobility, revealing systematic structural heterogeneity that traditional methods mask. The finding that geographic proximity does not guarantee temporal accessibility, exemplified by long commute times between neighbors, highlights a critical gap where spatial awareness conflicts with infrastructural reality—a tangible limitation on accessibility. The emergence of distinct, spatially coherent clusters suggests that mobility patterns are governed more by established socio-geographic structures (suburban development, river systems) than purely random travel choices. The distinction of Lisbon as a structural outlier implies a divergence in mobility governance or infrastructure density compared to its surroundings. This work demonstrates the complementary power of methodological fusion: process mining provides the granular sequencing data necessary for event reconstruction, while network science offers the analytical machinery to quantify the resulting complexity and structure of those sequences. The limitation noted—DFGs only capturing mode-destination transitions rather than full multimodal chains—points toward a necessary future direction in capturing true traveler experience beyond the immediate mode shift. What assumptions about centralized infrastructure planning underpin these observed clustering patterns? How can these dynamically defined clusters be used to formulate equitable investment strategies that address the temporal accessibility gaps identified between proximate municipalities?

Sentinel — Human

Confidence

The text exhibits the high density and specialized focus typical of published academic research, suggesting human authorship grounded in methodological expertise.

Signals Detected

Moderate sentence length variance and academic density typical of peer-reviewed work.

Strong logical flow linking methodology (process mining, network science) to findings (structural heterogeneity, clustering).

Use of specific statistical terms and clear delineation between methodology and results suggests authored expertise.

Citations to specific research methodologies (DFGs, process mining) and quantifiable metrics imply grounded data handling.

Human Indicators

The text employs precise, complex academic terminology ('Directly-Follows Graphs', 'Jensen–Shannon divergence') integrated seamlessly with the methodological narrative.

The admission of a specific limitation ('DFG structures represent only mode–destination transitions, not full multimodal trip chains, a limitation to be addressed in future works') is characteristic of genuine scholarly reflection.