Related papers: The evolution of navigable small-world networks
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…
Within the last fifteen years, network theory has been successfully applied both to natural sciences and to socioeconomic disciplines. In particular, bipartite networks have been recognized to provide a particularly insightful…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
Networks created and maintained by social processes, such as the human friendship network and the World Wide Web, appear to exhibit the property of navigability: namely, not only do short paths exist between any pair of nodes, but such…
We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With…
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…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition 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…
The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the…
The theory of random graphs goes back to the late 1950s when Paul Erd\H{o}s and Alfr\'ed R\'enyi introduced the Erd\H{o}s-R\'enyi random graph. Since then many models have been developed, and the study of random graph models has become…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
Network structures are extremely important to the study of political science. Much of the data in its subfields are naturally represented as networks. This includes trade, diplomatic and conflict relationships. The social structure of…
Navigation process is studied on a variant of the Watts-Strogatz small world network model embedded on a square lattice. With probability $p$, each vertex sends out a long range link, and the probability of the other end of this link…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
We prove logarithmic upper bounds for the diameters of the random-surfer Webgraph model and the PageRank-based selection Webgraph model, confirming the small world phenomenon holds for them. In the special case when the generated graph is a…
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…