Surfacic networks.

Surfacic networks are structures built upon a 2D manifold. Many systems, including transportation networks and various urban networks, fall into this category. The fluctuations of node elevations imply significant deviations from typical plane networks and require specific tools to understand their impact.

Stochastic block hypergraph model.

The stochastic block model is widely used to generate graphs with a community structure, but no simple alternative currently exists for hypergraphs, in which more than two nodes can be connected together through a hyperedge. We discuss here such a hypergraph generalization, based on the clustering connection probability P_{ij} between nodes of communities i and j, and that uses an explicit and modulable hyperedge formation process. We focus on the standard case where P_{ij}=pδ_{ij}+q(1-δ_{ij}) when 0≤q≤p (δ_{ij} is the Kronecker symbol).

Symmetry breaking in optimal transport networks.

Engineering multilayer networks that efficiently connect sets of points in space is a crucial task in all practical applications that concern the transport of people or the delivery of goods. Unfortunately, our current theoretical understanding of the shape of such optimal transport networks is quite limited. Not much is known about how the topology of the optimal network changes as a function of its size, the relative efficiency of its layers, and the cost of switching between layers.

Structure of road networks and the shape of the macroscopic fundamental diagram.

The macroscopic fundamental diagram (MFD) is a large-scale description of the traffic in an urban area and relates the average car flow to the average car density. This MFD has been observed empirically in several cities but how its properties are related to the structure of the road network has remained unclear so far. The MFD displays in general a maximum flow q^{*} for an optimal car density k^{*} which are crucial quantities for practical applications.

Stochastic equations and cities.

Stochastic equations constitute a major ingredient in many branches of science, from physics to biology and engineering. Not surprisingly, they appear in many quantitative studies of complex systems. In particular, this type of equation is useful for understanding the dynamics of urban population.

Scenarios for a post-COVID-19 world airline network.

The airline industry was severely hit by the COVID-19 crisis with an average demand decrease of about 64 % (IATA, April 2020), which triggered already several bankruptcies of airline companies all over the world. While the robustness of the world airline network (WAN) was mostly studied as a homogeneous network, we introduce a new tool for analyzing the impact of a company failure: the "airline company network" where two airlines are connected if they share at least one route segment. Using this tool, we observe that the failure of companies well connected with others has the largest impact on the connectivity of the WAN.

Evolution of road infrastructure in large urban areas.

Most cities in the United States and around the world were organized around car traffic. In particular, large structures such as urban freeways or ring roads were built for reducing car traffic congestion. With the evolution of public transportation and working conditions, the future of these structures and the organization of large urban areas is uncertain.

Class of models for random hypergraphs.

Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we introduce a class of models for random hypergraphs which displays a similar level of flexibility of complex network models and where the main ingredient is the probability that a node belongs to a hyperedge.

Spatial structure of city population growth.

We show here that population growth, resolved at the county level, is spatially heterogeneous both among and within the U.S. metropolitan statistical areas.

Betweenness centrality in dense spatial networks.

The betweenness centrality (BC) is an important quantity for understanding the structure of complex large networks. However, its calculation is in general difficult and known in simple cases only. In particular, the BC has been exactly computed for graphs constructed over a set of N points in the infinite density limit, displaying a universal behavior.

Local impacts on road networks and access to critical locations during extreme floods.

Floods affected more than 2 billion people worldwide from 1998 to 2017 and their occurrence is expected to increase due to climate warming, population growth and rapid urbanization. Recent approaches for understanding the resilience of transportation networks when facing floods mostly use the framework of percolation but we show here on a realistic high-resolution flood simulation that it is inadequate. Indeed, the giant connected component is not relevant and instead, we propose to partition the road network in terms of accessibility of local towns and define new measures that characterize the impact of the flooding event.

Emerging dynamics from high-resolution spatial numerical epidemics.

Simulating nationwide realistic individual movements with a detailed geographical structure can help optimise public health policies. However, existing tools have limited resolution or can only account for a limited number of agents. We introduce Epidemap, a new framework that can capture the daily movement of more than 60 million people in a country at a building-level resolution in a realistic and computationally efficient way.

Empirical evidence for a jamming transition in urban traffic.

Understanding the mechanisms leading to the formation and the propagation of traffic jams in large cities is of crucial importance for urban planning and traffic management. Many studies have already considered the emergence of traffic jams from the point of view of phase transitions, but mostly in simple geometries such as highways for example or in the framework of percolation where an external parameter is driving the transition. More generally, empirical evidence and characterization for a congestion transition in complex road networks are scarce, and here, we use traffic measures for Paris (France) during the period 2014-2018 for testing the existence of a jamming transition at the urban level.

From one-way streets to percolation on random mixed graphs.

In most studies, street networks are considered as undirected graphs while one-way streets and their effect on shortest paths are usually ignored. Here, we first study the empirical effect of one-way streets in about 140 cities in the world. Their presence induces a detour that persists over a wide range of distances and is characterized by a nonuniversal exponent.

The growth equation of cities.

The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most fundamental problem is to understand the hierarchical organization of city population and the statistical occurrence of megacities.

Access to mass rapid transit in OECD urban areas.

As mitigating car traffic in cities has become paramount to abate climate change effects, fostering public transport in cities appears ever-more appealing. A key ingredient in that purpose is easy access to mass rapid transit (MRT) systems. So far, we have however few empirical estimates of the coverage of MRT in urban areas, computed as the share of people living in MRT catchment areas, say for instance within walking distance.

Tomography of scaling.

Scaling describes how a given quantity that characterizes a system varies with its size . For most complex systems, it is of the form with a non-trivial value of the exponent , usually determined by regression methods. The presence of noise can make it difficult to conclude about the existence of a nonlinear behaviour with ≠ 1 and we propose here to circumvent fitting problems by investigating how two different systems of sizes and are related to each other.

Shape of shortest paths in random spatial networks.

In the classic model of first-passage percolation, for pairs of vertices separated by a Euclidean distance L, geodesics exhibit deviations from their mean length L that are of order L^{χ}, while the transversal fluctuations, known as wandering, grow as L^{ξ}. We find that when weighting edges directly with their Euclidean span in various spatial network models, we have two distinct classes defined by different exponents ξ=3/5 and χ=1/5, or ξ=7/10 and χ=2/5, depending only on coarse details of the specific connectivity laws used. Also, the travel-time fluctuations are Gaussian, rather than Tracy-Widom, which is rarely seen in first-passage models.

Critical factors for mitigating car traffic in cities.

Car traffic in urban systems has been studied intensely in past decades but models are either limited to a specific aspect of traffic or applied to a specific region. Despite the importance and urgency of the problem we have a poor theoretical understanding of the parameters controlling urban car use and congestion. Here, we combine economical and transport ingredients into a statistical physics approach and propose a generic model that predicts for different cities the share of car drivers, the CO2 emitted by cars and the average commuting time.

Optimal geometry of transportation networks.

Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network G of given length L that is optimal in a certain sense. In the general model, the optimality criterion is to minimize the average (over pairs of points chosen independently from the distribution) time to travel between the points, where a travel path consists of any line segments in the plane traversed at slow speed and any route within the subway network traversed at a faster speed. Of major interest is how the shape of the optimal network changes as L increases.

Efficiency and shrinking in evolving networks.

Characterizing the spatio-temporal evolution of networks is a central topic in many disciplines. While network expansion has been studied thoroughly, less is known about how empirical networks behave when shrinking. For transportation networks, this is especially relevant on account of their connection with the socio-economical substrate, and we focus here on the evolution of the French railway network from its birth in 1840 to 2000, in relation to the country's demographic dynamics.

From the betweenness centrality in street networks to structural invariants in random planar graphs.

The betweenness centrality, a path-based global measure of flow, is a static predictor of congestion and load on networks. Here we demonstrate that its statistical distribution is invariant for planar networks, that are used to model many infrastructural and biological systems. Empirical analysis of street networks from 97 cities worldwide, along with simulations of random planar graph models, indicates the observed invariance to be a consequence of a bimodal regime consisting of an underlying tree structure for high betweenness nodes, and a low betweenness regime corresponding to loops providing local path alternatives.

From global scaling to the dynamics of individual cities.

Scaling has been proposed as a powerful tool to analyze the properties of complex systems and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of urban datasets displays apparent nonlinear behaviors whose statistical validity and meaning were recently the focus of many debates. We discuss here another aspect, which is the implication of such scaling forms on individual cities and how they can be used for predicting the behavior of a city when its population changes.

Tracking random walks.

In empirical studies, trajectories of animals or individuals are sampled in space and time. Yet, it is unclear how sampling procedures bias the recorded data. Here, we consider the important case of movements that consist of alternating rests and moves of random durations and study how the estimate of their statistical properties is affected by the way we measure them.

Coalescing colony model: Mean-field, scaling, and geometry.

We analyze the coalescing model where a 'primary' colony grows and randomly emits secondary colonies that spread and eventually coalesce with it. This model describes population proliferation in theoretical ecology, tumor growth, and is also of great interest for modeling urban sprawl. Assuming the primary colony to be always circular of radius r(t) and the emission rate proportional to r(t)^{θ}, where θ>0, we derive the mean-field equations governing the dynamics of the primary colony, calculate the scaling exponents versus θ, and compare our results with numerical simulations.