Mobility and spatial networks 2

Migration drives urbanization, segregation, and socioeconomic change, yet internal migration remains underexplored compared to international migration. Modeling human mobility as networks, where nodes represent geographic regions and edges capture migration flows, enables the use of community detection methods to reveal structural patterns.Using Austria’s 2021 internal migration data, we applied the weighted Stochastic Block Model to uncover the modular structure of migration flows. Detected communities closely align with administrative boundaries, a novel finding validated through comparison with gravity model-based synthetic networks. These results suggest that administrative divisions significantly influence migration patterns beyond what mechanistic models predict.Extending this analysis to other countries, we find varying degrees of alignment, indicating context-dependent relationships between migration flows and administrative structures. This study emphasizes the value of advanced network methods in understanding internal migration dynamics.

Borders are prevalent in cities, conditioning mobility and shaping people's experience and sometimes aggravate social inequality through segregation. Past studies of mobility borders are limited to qualitative observations, anecdotal evidence, or static census data, providing only partial insights into how individuals navigate and experience the city through movement across different regions. In this work, we apply the unsupervised embedding method, specifically the skip-gram word2vec model towards human trajectory data to fill this gap. The dense representations of locations learned from word2vec model surpass traditional geographical metrics, revealing how demographic factors such as income influence urban connectivity. This approach allows us to identify 'borders' and 'bridges' that shape human mobility patterns, offering insights into the complex interplay between geographical and non-geographical factors. Our findings underscore the potential of data-driven methods to inform more inclusive urban planning and policy-making, highlighting the importance of considering both visible and invisible barriers in understanding the spatial dynamics of urban environments.

Extreme heat is a growing problem in European countries with rising temperatures and aging populations especially vulnerable to them. Research documents the consequences of high temperatures for economic growth and public health, but the effect of heat on the activities and behaviors that contribute to these consequences is less clear; with greater understanding of how populations react to heat waves, we can target policies to harden society against rising temperatures. Using rich mobility data that allows us to stratify according to age, gender, class and the type of activity, here we explore the consequences of extreme heat for mobility in Spain. Activity falls by as much as 8% on hot days and as much as 20% on hot afternoons, when temperatures are highest. People are less likely to forego frequent, routine activities relative to infrequent ones—and least likely to miss work. We identify significant differences across groups and activities, with the oldest most likely to avoid travel to work while cutting back most on other activities and the poorest are least likely to avoid travel to work—perhaps because they are least able to afford missing it, or perhaps because they are least able to work from home. Our results highlight the complex ways heat influences mobility and suggests hidden costs, from decreased foot traffic for restaurants to increased exposure to deleterious conditions for workers.

This study presents the first network analysis of a spatially detailed model of Roman roads, based on the most comprehensive and granular dataset to date (Brughmans et al., 2024). At its peak, the Roman Empire spanned more than 5 million km^2 across Europe, North Africa, and the Middle East, supported by an extensive transportation network that facilitated commerce, communication, and military operations. Although rivers and seas provided efficient long-distance transport, roads were essential for connecting inland areas and enabling effective short- to mid-distance travel.We model the Empire's road networks, as well as those of individual Roman provinces, as spatial graphs, with nodes corresponding to settlements or road intersections and edges representing road segments. We perform an exploratory network analysis. Roads are revealed to have low sinuosity in general, supporting the long-held assumption that Roman roads were relatively straight. The networks have small clustering coefficient, and vary in density from region to region, with the Empire overall including 46% of the theoretically possible road segments (gamma index).We then estimate interurban traffic, a key component of overall road use, using spatial interaction models, integrating settlement population estimates with travel time estimates based on road length and terrain slope (Fig.~1a). The models estimate higher traffic flows on road segments identified by archaeologists as historically significant. These findings remain robust even after the removal of up to 30\% of road segments classified as uncertain in the archaeological literature (Fig.~1b). These insights into the structure of past terrestrial mobility in Europe, North Africa, and the Middle East demonstrate the effectiveness of network-based approaches in revealing Roman transportation dynamics and are crucial for understanding the long-term development of mobility in the area.

Infrastructure networks are crucial for enabling human mobility across almost all modes of transport. However, designing efficient transport networks is a complex problem due to the mutual dependencies between the structure and usage of the network. For example, improving one link in the network may alter route choices of travelers and thereby also affect the usage and importance of all other links. Understanding the synergies and the importance of individual links is a fundamental prerequisite for efficient network extension planning. Common route choice models, however, are often not well suited to this task. Shortest path routing typically oversimplifies route choices and discrete choice models require predefined routing options, not suitable for network planning tasks where efficient routing options vary over time. Here, we analytically quantify the importance of individual links and the synergy of multiple links in transport networks by exploiting a recently proposed perturbed utility route choice model based on optimal flow assignment. By describing the route changes in response to the improvement of individual links as cycle flows in the network, we analytically track the optimal flow solution and the changes in overall network quality. This enables us to directly quantify the importance of individual links as the derivative of the total network quality with respect to the change in link quality. Additionally, higher order derivatives capture synergies between different links in the network. We apply this approach to bike path network planning and demonstrate potential applications to automatically generate efficient prioritization of bike path network extensions and identify synergistic corridors for bike highways in urban street networks.Our results may help to improve the quantitative evaluation of complex interactions and synergies in transport and infrastructure networks and support efficient network extension planning.

Random Spatial Networks (RSNs), including Random Geometric Graphs (RGG), Soft RGG, and Gabriel Graphs, model systems embedded in physical space such as communication and transportation networks. A fundamental challenge in RSNs is understanding shortest path distances, which are crucial for optimizing routing and analyzing network robustness.This study develops a probabilistic framework for shortest path distances in RSNs. Using the Central Limit Theorem, we show that the Euclidean distances of nodes at a shortest path distance t from a given node u follow a normal distribution, N(μ_t, σ_t), with both μ_t and σ_t^2 growing linearly with t. Explicit formulas for these parameters are provided for RGGs. We establish a relationship between Euclidean and shortest path distances, enabling computation of the probability:Pr[dist(u, v) = t | |u - v|] = Φ((|u - v| - μ_{t-1}) / σ_{t-1}) - Φ((|u - v| - μ_t) / σ_t),where Φ(x) is the cumulative distribution function (CDF) of the standard normal distribution.Additionally, leveraging the probabilistic relationship between shortest path components, we propose a shortest path field model that predicts shortest path node distributions. This model, validated through simulations, demonstrates high accuracy in RSNs with high average degree.