Related papers: Small-worlds: How and why
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…
We study the dynamical behaviour of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties…
Researchers have long observed that the ``small-world" property, which combines the concepts of high transitivity or clustering with a low average path length, is ubiquitous for networks obtained from a variety of disciplines, including…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Advances in the next generation of mesoscopic electronics require an understanding of topological phases in inhomogeneous media and the principles that govern them. Motivated by the nature of motifs available in printable conducting inks,…
Networks such as organizational network of a global company play an important role in a variety of knowledge management and information diffusion tasks. The nodes in these networks correspond to individuals who are self-interested. The…
We consider the size and structure of the automorphism groups of a variety of empirical `real-world' networks and find that, in contrast to classical random graph models, many real-world networks are richly symmetric. We relate automorphism…
Intrigued by the capacity of random networks, we start by proving a max-flow min-cut theorem that is applicable to any random graph obeying a suitably defined independence-in-cut property. We then show that this property is satisfied by…
As more connectome data become available, the question of how to best analyse the structure of biological neural networks becomes increasingly pertinent. In brain networks, knowing that two areas are connected is often not sufficient, as…
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…
We investigate the emergence and persistence of communities through a recently proposed mechanism of adaptive rewiring in coevolutionary networks. We characterize the topological structures arising in a coevolutionary network subject to an…
How does one make acquaintances? A simple observation from everyday experience is that often one of our acquaintances introduces us to one of his acquaintances. Such a simple triangle interaction may be viewed as the basis of the evolution…
Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or…
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the…
Through an eigenanalysis of small perturbations, as typically done in small-signal stability studies, we intend to discover the underlying reasons that make those perturbations propagate in some way or another in the grid. To this end, we…
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…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
Understanding the topological characteristics of complex networks and how they affect navigability is one of the most important goals in science today, as it plays a central role in various economic, biological, ecological and social…
We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us…
Real-world network systems are inherently dynamic, with network topologies undergoing continuous changes over time. Previous works often focus on static networks or rely on complete prior knowledge of evolving topologies, whereas real-world…