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Related papers: Degree-distribution Stability of Growing Networks

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In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…

Social and Information Networks · Computer Science 2016-11-04 Masaki Ogura , Victor M. Preciado

In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous…

Physics and Society · Physics 2009-10-08 David M. D. Smith , Jukka-Pekka Onnela , Nick S. Jones

Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…

Mathematical Physics · Physics 2007-05-23 Dinghua Shi , Liming Liu , Xiang Zhu , Huijie Zhou , Binbin Wang

In this paper, we provide a general method to obtain the exact solutions of the degree distributions for RBDN with network size decline. First by stochastic process rules, the steady state transformation equations and steady state degree…

Physics and Society · Physics 2016-02-10 Xiaojun Zhang , Huilan Yang

We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…

Physics and Society · Physics 2009-07-10 Tomas Hruz , Michal Natora , Madhuresh Agrawal

We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…

Statistical Mechanics · Physics 2007-09-14 Henrik Jeldtot Jensen

The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current…

Combinatorics · Mathematics 2024-01-09 Péter L. Erdős , Tamás Róbert Mezei , István Miklós

Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential…

Statistical Mechanics · Physics 2007-05-23 Simon Laird , Henrik Jeldtoft Jensen

One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…

Data Structures and Algorithms · Computer Science 2011-09-01 Isabelle Stanton , Ali Pinar

Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…

Social and Information Networks · Computer Science 2012-11-01 J. Ray , A. Pinar , C. Seshadhri

Discrete-time discrete-state finite Markov chains are versatile mathematical models for a wide range of real-life stochastic processes. One of most common tasks in studies of Markov chains is computation of the stationary distribution.…

Numerical Analysis · Mathematics 2022-09-07 Konstantin Avrachenkov , Patrick Brown , Nelly Litvak

One of the proposed solutions to the equilibrium selection problem for agents learning in repeated games is obtained via the notion of stochastic stability. Learning algorithms are perturbed so that the Markov chain underlying the learning…

Computer Science and Game Theory · Computer Science 2012-07-09 John Wicks , Amy Greenwald

Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on…

Physics and Society · Physics 2009-11-13 Luca Dall'Asta

A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…

Adaptation and Self-Organizing Systems · Physics 2016-06-28 H. Silk , M. Homer , T. Gross

We compute the stationary distribution of a continuous-time Markov chain which is constructed by gluing together two finite, irreducible Markov chains by identifying a pair of states of one chain with a pair of states of the other and…

Probability · Mathematics 2015-10-22 Bence Mélykúti , Peter Pfaffelhuber

We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social…

Information Retrieval · Computer Science 2009-04-18 Dusko Pavlovic

There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network;…

Statistical Mechanics · Physics 2013-10-24 Brian Karrer , Gourab Ghoshal

Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…

Statistical Mechanics · Physics 2009-11-13 M. O. Hase , J. F. F. Mendes

The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…

Physics and Society · Physics 2025-07-11 Jonathan Franceschi , Lorenzo Pareschi , Mattia Zanella

In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…

Combinatorics · Mathematics 2014-01-07 Linda Farczadi , Nicholas Wormald