Related papers: Degree-distribution Stability of Growing Networks
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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;…
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…
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…
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…