Related papers: A long-time limit of world subway networks
Urban transportation systems grow over time as city populations grow and move and their transportation needs evolve. Typical network growth models, such as preferential attachment, grow the network node by node whereas rail and metro…
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…
Subway systems span most large cities, and railway networks most countries in the world. These networks are fundamental in the development of countries and their cities, and it is therefore crucial to understand their formation and…
Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or…
One of the most important features of spatial networks such as transportation networks, power grids, Internet, neural networks, is the existence of a cost associated with the length of links. Such a cost has a profound influence on the…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
We study how the graph structure of the Internet at the Autonomous Systems (AS) level evolved during a decade. For each year of the period 2008-2017 we consider a snapshot of the AS graph and examine how many features related to structure,…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
Complex networks have certain properties that distinguish them from their respective uniform or regular counterparts. One of these properties is the variation of topological properties along different hierarchical levels. In this work, we…
The urban networks of London and New York City are investigated as directed graphs within the paradigm of graph percolation. It has been recently observed that urban networks show a critical percolation transition when a fraction of edges…
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…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…
How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…
We consider a regular embedded network composed by two curves, one of them closed, in a convex domain $\Omega$. The two curves meet only in one point, forming angle of $120$ degrees. The non-closed curve has a fixed end point on…
Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy.…
We study network properties of networks evolving in time based on optimal transport principles. These evolve from a structure covering uniformly a continuous space towards an optimal design in terms of optimal transport theory. At…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
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…
Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…