相关论文: Harmony in the Small-World
Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique…
A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most…
We introduce and define three types of small worlds: small worlds based on the diameter of the network (SWD), those based on the average geodesic distance between nodes (SWA), and those based on the median geodesic distance (SWMd). These…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…
According to the small-world concept, the entire world is connected through short chains of acquaintances. In popular imagination this is captured in the phrase six degrees of separation, implying that any two individuals are, at most, six…
In this article we discuss six degrees of separation, which has been proposed by Milgram, from a theoretical point of view. Simply if one has $k$ friends, the number $N$ of indirect friends goes up to $\sim k^d$ in $d$ degrees of…
Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a small-world. Here, we test the…
A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the…
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…
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 believed that almost any pair of people in the world can be connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the ``six degrees of…
Recently Watts and Strogatz have given an interesting model of small-world networks. Here we concretise the concept of a ``far away'' connection in a network by defining a {\it far edge}. Our definition is algorithmic and independent of…
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…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation…
Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such…
Discoveries of the scale-free and small-world features are reported on a network constructed from the seismic data. It is shown that the connectivity distribution decays as a power law, and the value of the degrees of separation, i.e., the…
We investigate small-world networks from the point of view of their origin. While the characteristics of small-world networks are now fairly well understood, there is as yet no work on what drives the emergence of such a network…
The small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)] has attracted much interests in studying the interesting properties of the networks without time-delay. However, a signal or influence travelling on…