Related papers: The evolution of navigable small-world networks
Small-world graphs, which combine randomized and structured elements, are seen as prevalent in nature. Jon Kleinberg showed that in some graphs of this type it is possible to route, or navigate, between vertices in few steps even with very…
The Small World phenomenon has inspired researchers across a number of fields. A breakthrough in its understanding was made by Kleinberg who introduced Rank Based Augmentation (RBA): add to each vertex independently an arc to a random…
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 algorithmic small-world phenomenon, empirically established by Milgram's letter forwarding experiments from the 60s, was theoretically explained by Kleinberg in 2000. However, from today's perspective his model has several severe…
Continuing in the steps of Jon Kleinberg's and others celebrated work on decentralized search in small-world networks, we conduct an experimental analysis of a dynamic algorithm that produces small-world networks. We find that the algorithm…
One of the key features of small-worlds is the ability to route messages with few hops only using local knowledge of the topology. In 2000, Kleinberg proposed a model based on an augmented grid that asymptotically exhibits such property. In…
Numerous studies show that most known real-world complex networks share similar properties in their connectivity and degree distribution. They are called small worlds. This article gives a method to turn random graphs into Small World…
Dating back to two famous experiments by the social-psychologist, Stanley Milgram, in the 1960s, the small-world phenomenon is the idea that all people are connected through a short chain of acquaintances that can be used to route messages.…
Navigability of networks, that is the ability to find any given destination vertex starting from any other vertex, is crucial to their usefulness. In 2000 Kleinberg showed that optimal navigability could be achieved in small-world networks…
In recent work, Jon Kleinberg considered a small-world network model consisting of a d-dimensional lattice augmented with shortcuts. The probability of a shortcut being present between two points decays as a power of the distance between…
This paper mainly investigates why small-world networks are navigable and how to navigate small-world networks. We find that the navigability can naturally emerge from self-organization in the absence of prior knowledge about underlying…
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…
Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…
We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable…
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…
This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…
We propose a simple growing model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new nodes are made locally to the creator and its nearest neighbors. It is found…
We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically…