Related papers: Spatial small-world networks: A wiring-cost perspe…
Quantitative descriptions of network structure in big data can provide fundamental insights into the function of interconnected complex systems. Small-world structure, commonly diagnosed by high local clustering yet short average path…
It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be…
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…
Small world models are networks consisting of many local links and fewer long range `shortcuts'. In this paper, we consider some particular instances, and rigorously investigate the distribution of their inter--point network distances. Our…
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural…
We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies…
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…
Small-world networks, i.e. networks displaying both a high clustering coefficient and a small characteristic path length, are obliquitous in nature. Since their identification, the "small-worldness" metric, as proposed by Humphries and…
One of the challenges for future infrastructures is how to design a network with high efficiency and strong connectivity at low cost. We propose self-organized geographical networks beyond the vulnerable scale-free structure found in many…
Small world models are networks consisting of many local links and fewer long range 'shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution…
Small-world networks are highly clustered networks with small average distance among the nodes. There are many natural and technological networks that present this kind of connections. The on-off intermittency is investigated in small-world…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes…
Link weight is crucial in weighted complex networks. It provides additional dimension for describing and adjusting the properties of networks. The topological role of weight is studied by the effects of random redistribution of link weights…
Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing…
Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current…