Related papers: Scale-free Segregation in Transport Networks
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous integrable models out of equilibrium. We…
We review two models of optimal transport, where congestion effects during the transport can be possibly taken into account. The first model is Beckmann's one, where the transport activities are modeled by vector fields with given…
We present the distance matrix evolution for different types of networks: exponential, scale-free and classical random ones. Statistical properties of these matrices are discussed as well as topological features of the networks. Numerical…
The efficiency of graph-based semi-supervised algorithms depends on the graph of instances on which they are applied. The instances are often in a vectorial form before a graph linking them is built. The construction of the graph relies on…
Recently, motivated by the pioneer works in revealing the small-world effect and scale-free property of various real-life networks, many scientists devote themselves to studying complex networks. In this paper, we give a brief review on the…
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
Understanding the dynamics of traffic clusters is crucial for enhancing urban transportation systems, particularly in managing congestion and free-flow states. This study applies computational percolation theory to analyze the formation and…
Large scale traffic networks are an indispensable part of contemporary human mobility and international trade. Networks of airport travel or cargo ships movements are invaluable for the understanding of human mobility…
Isolation is one of the more relevant attributes associated to the idea of network slicing, introduced by 5G services. Through isolation it is expected that slices from different customers could gracefully coexist without interfering each…
To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…
The coupling of scale-free networks with mobile unstructured networks is certainly unusual. In mobile networks, connections active at a given instant are constrained by the geographical distribution of mobile nodes, and by the limited…
The behaviour of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable…
The urban road networks of the 20 largest German cities have been analysed, based on a detailed database providing the geographical positions as well as the travel-times for network sizes up to 37,000 nodes and 87,000 links. As the human…
We study the evolution of a random graph under the constraint that the diameter remain constant as the graph grows. We show that if the graph maintains the form of its link distribution it must be scale-free with exponent between 2 and 3.…
We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We…
Segregation is a highly nuanced concept that researchers have worked to define and measure over the past several decades. Conventional approaches tend to estimate segregation based on residential patterns in a static manner. In this work,…
We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned…
Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…