Related papers: Rank-dependent deactivation in network evolution

In many real world networks, the number of links increases nonlinearly with the number of nodes. Models of such accelerated growth have been considered earlier with deterministic and stochastic number of links. Here we consider stochastic…

Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…

We investigate choice-driven network growth. In this model, nodes are added one by one according to the following procedure: for each addition event a set of target nodes is selected, each according to linear preferential attachment, and a…

Recurrent neural networks (RNNs) trained on low-dimensional tasks have been widely used to model functional biological networks. However, the solutions found by learning and the effect of initial connectivity are not well understood. Here,…

Discriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. The rules governing this growth are attributed to mechanisms…

Modeling biological networks serves as both a major goal and an effective tool of systems biology in studying mechanisms that orchestrate the activities of gene products in cells. Biological networks are context specific and dynamic in…

We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of…

In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…

A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…

The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we…

Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…

There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…

Memory plays a vital role in the temporal evolution of interactions of complex systems. To address the impact of memory on the temporal pattern of networks, we propose a simple preferential connection model, in which nodes have a…

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…

We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…

Most real world dynamic networks are evolved very fast with time. It is not feasible to collect the entire network at any given time to study its characteristics. This creates the need to propose local algorithms to study various properties…

Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks…

Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…

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…