Related papers: Master-equation analysis of accelerating networks

Motivated by data on the evolution of the Internet and World Wide Web we consider scenarios of self-organization of the nonlinearly growing networks into free-scale structures. We find that the accelerating growth of the networks…

In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…

This paper establishes a relation between scale-free networks and Markov chains, and proposes a computation framework for degree distributions of scale-free networks. We first find that, under the BA model, the degree evolution of…

The model of scientific paradigms spreading throughout the community of agents with memory is analyzed using the master equation. The case of two competing ideas is considered for various networks of interactions, including agents placed at…

Many real-world networks have properties of small-world networks, with clustered local neighborhoods and low average-shortest path (ASP). They may also show a scale-free degree distribution, which can be generated by growth and preferential…

Numerous works have been proposed to generate random graphs preserving the same properties as real-life large scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs…

We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…

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…

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a…

In this paper, we propose a novel distributed algorithm for consensus optimization over networks and a robust extension tailored to deal with asynchronous agents and packet losses. Indeed, to robustly achieve dynamic consensus on the…

We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a new preferential-attachment scheme, in which a new node attaches to an existing node i with…

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…

One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number…

Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…

Understanding the evolution of cooperation in structured populations represented by networks is a problem of long research interest, and a most fundamental and widespread property of social networks related to cooperation phenomena is that…

The ability to model and predict ego-vehicle's surrounding traffic is crucial for autonomous pilots and intelligent driver-assistance systems. Acceleration prediction is important as one of the major components of traffic prediction. This…

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…

Many of the biological, social and man-made networks around us are inherently dynamic, with their links switching on and off over time. The evolution of these networks is often non-Markovian, and the dynamics of their links correlated.…

Real-world networks grow over time; statistical models based on node exchangeability are not appropriate. Instead of constraining the structure of the \textit{distribution} of edges, we propose that the relevant symmetries refer to the…