Related papers: From one-way streets to percolation on random mixe…
A new random geometric graph model, the so-called secrecy graph, is introduced and studied. The graph represents a wireless network and includes only edges over which secure communication in the presence of eavesdroppers is possible. The…
Urban transportation systems are vulnerable to congestion, accidents, weather, special events, and other costly delays. Whereas typical policy responses prioritize reduction of delays under normal conditions to improve the efficiency of…
Great cities connect people; failed cities isolate people. Despite the fundamental importance of physical, face-to-face social-ties in the functioning of cities, these connectivity networks are not explicitly observed in their entirety.…
A graphical model provides a compact and efficient representation of the association structure of a multivariate distribution by means of a graph. Relevant features of the distribution are represented by vertices, edges and other…
Since its recent introduction, the small-world effect has been identified in several important real-world systems. Frequently, it is a consequence of the existence of a few long-range connections, which dominate the original regular…
We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…
We study the impact of global traffic light control strategies in a recently proposed cellular automaton model for vehicular traffic in city networks. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
We investigate the behaviour of the shortest path on a directed two-dimensional square lattice for bond percolation at the critical probability $p_c$ . We observe that flipping an edge lying on the shortest path has a non-local effect in…
We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs as well as random graphs, and investigate their relations to classical percolation theory, more particularly the impact of Bernoulli bond…
We study the asymptotic behavior of the number of paths of length $N$ on several classes of infinite graphs with a single special vertex. This vertex can work as an entropic trap for the path, i.e. under certain conditions the dominant part…
We present a study of site and bond percolation on periodic lattices with (on average) fewer than three nearest neighbors per site. We have studied this issue in two contexts: By simulating oxides with a mixture of 2-coordinated and…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
Many real-world networks exhibit the so-called small-world phenomenon: their typical distances are much smaller than their sizes. One mathematical model for this phenomenon is a long-range percolation graph on a $d$-dimensional box $\{0, 1,…
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…
We propose a road layout and traffic model, based on last passage percolation (LPP). An easy naive argument shows that coalescence of traffic trajectories is essential to be considered when observing traffic networks around us. This is a…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…