Related papers: Scale Invariance in Road Networks
We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of…
We examine the extent of needless traffic exposure by the routing infrastructure to nations geographically irrelevant to packet transmission. We quantify what countries are geographically logical to observe on a network path traveling…
We study the growth of London's street-network in its dual representation, as the city has evolved over the last 224 years. The dual representation of a planar graph is a content-based network, where each node is a set of edges of the…
We report the statistical properties of three bus-transport networks (BTN) in three different cities of China. These networks are composed of a set of bus lines and stations serviced by these. Network properties, including the degree…
In this article, we study transportation network in Minnesota. We show that the system is characterized by Taylor's power law for fluctuation scaling with nontrivial values of the scaling exponent. We also show that the characteristic…
Metcalfe's Law captures the relationship between the value of a network and its scale, asserting that a network's value is directly proportional to the square of its size. Over the past four decades, various researchers have proposed…
Road network representation learning aims to learn compressed and effective vectorized representations for road segments that are applicable to numerous tasks. In this paper, we identify the limitations of existing methods, particularly…
A set of general allometric scaling laws is derived for different systems represented by tree networks. The formulation postulates self-similar networks with an arbitrary number of branches developed in each generation, and with an…
Because of increasing global urbanization and its immediate consequences, including changes in patterns of food demand, circulation and land use, the next century will witness a major increase in the extent of paved roads built worldwide.…
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological…
Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
Public transport systems in 22 Polish cities have been analyzed. Sizes of these networks range from N=152 to N=2881. Depending on the assumed definition of network topology the degree distribution can follow a power law or can be described…
The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…
Let $G$ be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on $G$. Fix vertices $u$ and $v$ and consider the set of paths that start at $u$ and end at $v$, self-intersecting in any number of…
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct…
We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular ($A/L \times L)$ landscape and, once reached, they…
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of…
Social network structure is very important for understanding human information diffusing, cooperating and competing patterns. It can bring us with some deep insights about how people affect each other. As a part of complex networks, social…
Reliable electricity supply depends on the seamless operation of high-voltage grid infrastructure spanning both transmission and sub-transmission levels. Beneath this apparent uniformity lies a striking structural diversity, which leaves a…