Related papers: On the growth of a superlinear preferential attach…
A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential…
We discuss a model for evolutionary game dynamics in a growing, network-structured population. In our model, new players can either make connections to random preexisting players or preferentially attach to those that have been successful…
We introduce a new model of preferential attachment with fitness, and establish a time reversed duality between the model and a system of branching-coalescing particles. Using this duality, we give a clear and concise explanation for the…
Consider a generalised preferential attachment tree with attachment function $f$, that is a random tree, where at each time-step a node connects to an existing node $v$ with probability proportional to $f(\mathrm{deg}(v))$, where…
We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its barycenter. Each new site is fixed in space by…
In this paper we define a family of preferential attachment models for random graphs with fitness in the following way: independently for each node, at each time step a random fitness is drawn according to the position of a moving average…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
Preferential attachment probabilities scheme appear in the context of scale free random graphs [1],[2]. In this work we present preferential attachment probabilities scheme as a sequence of dependent Bernoulli random variables and we give…
The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $\alpha_1$, a new vertex $x_t$ and $m$ edges…
Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by…
The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules…
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional…
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…
In order to better understand dynamical functions on amounts of natural and man-made complex systems, lots of researchers from a wide range of disciplines, covering statistic physics, mathematics, theoretical computer science, and so on,…
We study structural properties of trees grown by preferential attachment. In this mechanism, nodes are added sequentially and attached to existing nodes at a rate that is strictly proportional to the degree. We classify nodes by their depth…
Preferential attachment is a popular generative mechanism to explain the widespread observation of power law distributed networks. We introduce an alternative explanation for the phenomenon by allowing the link growth rates to vary across…
We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to…