Related papers: Modulated Scale-free Network in the Euclidean Spac…
The Barab\'{a}si-Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability $p$, we add a new node with $m$ edges which preferentially link to the nodes presented in the…
We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…
We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and…
Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…
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…
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…
A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
In this work we study a simple evolutionary model of bipartite networks which its evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the above evolutionary…
We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular…
We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent…
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…
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…
In this paper we present a deterministic vertex spawning model that yields a scale-free network. The model specifies that a parent vertex produces a child vertex in a time interval approximately proportional to the current time and…
Uncorrelated random scale-free networks are useful null models to check the accuracy an the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable to generate random uncorrelated…
Many networks exhibit scale free behavior where their degree distribution obeys a power law for large vertex degrees. Models constructed to explain this phenomena have relied on preferential attachment where the networks grow by the…
In a previous Letter (cond-mat/0106565), Goh et al have presented a numerical study of the load--or betweenness centrality--distribution in a scale-free network whose degree distribution follows a power law with a tunable exponent $\gamma$.…
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 scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units…
We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…