Related papers: Spatial networks evolving to reduce length
Empirical studies on the spatial structures in several real transport networks reveal that the distance distribution in these networks obeys power law. To discuss the influence of the power-law exponent on the network's structure and…
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 systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
The minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on trees in polynomial…
Network visualization is essential for many scientific, societal, technological and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication and…
Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street…
Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…
We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical…
Suppose that under the action of gravity, liquid drains through the unit $d$-cube via a minimal-length network of channels constrained to pass through random sites and to flow with nonnegative component in one of the canonical orthogonal…
Small-world networks, which combine randomized and structured elements, are seen as prevalent in nature. Several random graph models have been given for small-world networks, with one of the most fruitful, introduced by Jon Kleinberg,…
The spectral evolution model aims to characterize the growth of large networks (i.e., how they evolve as new edges are established) in terms of the eigenvalue decomposition of the adjacency matrices. It assumes that, while eigenvectors…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
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…
A social network grows over a period of time with the formation of new connections and relations. In recent years we have witnessed a massive growth of online social networks like Facebook, Twitter etc. So it has become a problem of extreme…
We study the formation and evolution of an interconnected string network in large-scale field-theory numerical simulations, both in flat spacetime and in expanding universe. The network consists of gauge U(1) strings of two different kinds…
Inspired by the structure of technological networks, we discuss network evolution mechanisms which give rise to topological properties found in real spatial networks. Thus, the peculiar structure of transport and distribution networks is…
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…
Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
In a highly influential paper twenty years ago, Barab\'asi and Albert [Science 286, 509 (1999)] showed that networks undergoing generic growth processes with preferential attachment evolve towards scale-free structures. In any finite…