Related papers: Evolving networks through deletion and duplication
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…
We show that the protein-protein interaction networks can be surprisingly well described by a very simple evolution model of duplication and divergence. The model exhibits a remarkably rich behavior depending on a single parameter, the…
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…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…
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…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
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.…
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…
We study a discrete-time duplication-deletion random graph model and analyse its asymptotic degree distribution. The random graphs consists of disjoint cliques. In each time step either a new vertex is brought in with probability $0<p<1$…
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…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
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…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…
Gene-sharing networks provide a powerful framework to study the evolution of viruses and mobile genetic elements. These bipartite networks, which link genes to the genomes that contain them, exhibit characteristic degree distributions: a…
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…
Genomic duplication-divergence events, which are the primary source of new protein functions, occur stochastically at a wide range of genomic scales, from single gene to whole genome duplications. Clearly, this fundamental evolutionary…
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…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…