Related papers: Anomalous scaling in redirection networks

In a recent paper, Krapivsky and Redner (Phys. Rev. E, 71 (2005) 036118) proposed a new growing network model with new nodes being attached to a randomly selected node, as well to all ancestors of the target node. The model leads to a…

We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with…

We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already…

How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…

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…

In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…

We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on…

We study a random recursive tree model featuring complete redirection called the random friend tree and introduced by Saram\"aki and Kaski. Vertices are attached in a sequential manner one by one by selecting an existing target vertex and…

A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…

The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…

The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively and linking each to an earlier node of degree k with attachment probability A_k. When A_k grows slower…

We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…

We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the…

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…

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…

Growing networks have a causal structure. We show that the causality strongly influences the scaling and geometrical properties of the network. In particular the average distance between nodes is smaller for causal networks than for…

In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific…

A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of…