Related papers: Networks become navigable as nodes move and forget
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…
In the 1960s, the social scientist Stanley Milgram performed his famous "small-world" experiments where he found that people in the US who are far apart geographically are nevertheless connected by remarkably short chains of acquaintances.…
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…
Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical…
Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods…
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…
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…
We revisit two evolutionary game theory models, namely the Prisoner and the Snowdrift dilemmas, on top of small-world networks. These dynamics on networked populations (individuals occupying nodes of a graph) are mainly concerning on the…
For a sensor network, a tractable spatially-dependent node deployment model is presented with the property that the density is inversely proportional to the sink distance. A stochastic model is formulated to examine message advancements…
Navigation on graphs is the problem how an agent walking on the graph can get from a source to a target with limited information about the graph. The information and the way to exploit it can vary. In this paper, we study navigation on…
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…
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…
Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…