Related papers: Small-World Propensity in Weighted, Real-World Net…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
The small-world property in the context of complex networks implies structural benefits to the processes taking place within a network, such as optimal information transmission and robustness. In this paper, we study a model network of…
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…
A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behaviour. The inference process is often done by using bi-variate similarity measures, such as 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 Watts-Strogatz model (WS) has been demonstrated to effectively describe real-world networks due to its ability to reproduce the small-world properties commonly observed in a variety of systems, including social networks, computer…
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…
Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
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…
We study two kinds of weighted networks, weighted small-world (WSW) and weighted scale-free (WSF). The weight $w_{ij}$ of a link between nodes $i$ and $j$ in the network is defined as the product of endpoint node degrees; that is…
Complex network formalism allows to explain the behavior of systems composed by interacting units. Several prototypical network models have been proposed thus far. The small-world model has been introduced to mimic two important features…
It is commonly known that there exist short paths between vertices in a network showing the small-world effect. Yet vertices, for example, the individuals living in society, usually are not able to find the shortest paths, due to the very…
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 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…
The functional consequences of local and global dynamics can be very different in natural systems. Many such systems have a network description that exhibits strong local clustering as well as high communication efficiency, often termed as…
A number of recent studies have focused on the statistical properties of networked systems such as social networks and the World-Wide Web. Researchers have concentrated particularly on a few properties which seem to be common to many…
We proposed a deterministic multidimensional growth model for small-world networks. The model can characterize the distinguishing properties of many real-life networks with geometric space structure. Our results show the model possesses…
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…
The Small-World phenomenon, popularly known as six degrees of separation, has been mathematically formalized by Watts and Strogatz in a study of the topological properties of a network. Small-worlds networks are defined in terms of two…