Related papers: Co-evolving dynamic networks
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
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…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation…
Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of…
There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
We propose a model of network growth in which the network is co-evolving together with the dynamics of a quantum mechanical system, namely a quantum walk taking place over the network. The model naturally generalizes the Barab\'{a}si-Albert…
We investigate a growing network model that combines preferential and uniform attachment with two distinct mechanisms of edge deletion. In addition to the usual uniform probability edge deletion, we introduce a novel node-based rule in…
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…
Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
We study a simple model of dynamic networks, characterized by a set preferred degree, $\kappa$. Each node with degree $k$ attempts to maintain its $\kappa$ and will add (cut) a link with probability $w(k;\kappa)$ ($1-w(k;\kappa)$). As a…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…
Motivated by questions in social networks, distributed computing and probabilistic combinatorics, the last few years have seen increasing interest in network evolution models where new vertices entering the system need to make decisions…