Related papers: Sublinear but Never Superlinear Preferential Attac…
Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However,…
We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…
We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses $r$ vertices…
Many real-world systems are profitably described as complex networks that grow over time. Preferential attachment and node fitness are two simple growth mechanisms that not only explain certain structural properties commonly observed in…
When nodes can repeatedly update their behavior (as in agent-based models from computational social science or repeated-game play settings) the problem of optimal network seeding becomes very complex. For a popular spreading-phenomena model…
We propose a model that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the…
Preferential attachment networks are a type of random network where new nodes are connected to existing ones at random, and are more likely to connect to those that already have many connections. We investigate further a family of models…
In this paper we introduce a new type of preferential attachment network, the growth of which is based on the eigenvalue centrality. In this network, the agents attach most probably to the nodes with larger eigenvalue centrality which…
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 introduce a model for directed spatial networks. Starting from an age-based preferential attachment model in which all arcs point from younger to older vertices, we add \emph{reciprocal} connections whose probabilities depend on the age…
Let $P=\{p_0,\ldots,p_{n-1}\}$ be a set of points in $\mathbb{R}^d$, modeling devices in a wireless network. A range assignment assigns a range $r(p_i)$ to each point $p_i\in P$, thus inducing a directed communication graph $G_r$ in which…
The results of training a neural network are heavily dependent on the architecture chosen; and even a modification of only its size, however small, typically involves restarting the training process. In contrast to this, we begin training…
We propose a model of a growing network, in which preferential linking is combined with partial inheritance of connectivity (number of incoming links) of individual nodes by new ones. The nontrivial version of this model is solved exactly…
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…
In this paper, we introduce a novel concept for learning of the parameters in a neural network. Our idea is grounded on modeling a learning problem that addresses a trade-off between (i) satisfying local objectives at each node and (ii)…
Every network scientist knows that preferential attachment combines with growth to produce networks with power-law in-degree distributions. How, then, is it possible for the network of American Physical Society journal collection citations…
We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…
We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination…
We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that…
Under preferential attachment (PA) network growth models late arrivals are at a disadvantage with regard to their final degrees. Previous extensions of PA have addressed this deficiency by either adding the notion of node fitness to PA,…