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In the study of epidemic dynamics a fundamental question is whether a pathogen initially affecting only one individual will give rise to a limited outbreak or to a widespread pandemic. The answer to this question crucially depends not only…

Physics and Society · Physics 2021-08-12 Alfredo De Bellis , Romualdo Pastor-Satorras , Claudio Castellano

In this paper, we characterise the notion of preferential attachment in networks as action at a distance, and argue that it can only be an emergent phenomenon -- the actual mechanism by which networks grow always being the closing of…

Social and Information Networks · Computer Science 2017-04-25 Jérôme Kunegis , Fariba Karimi , Jun Sun

Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…

In this article we discuss network growth based on Prisoner's Dilemma(PD) where palyers on nodes in a network palay with its linked players. The players estimate total profits in the PD. When a new node is attached, the node make linkes to…

Physics and Society · Physics 2009-09-29 Norihito Toyota

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…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Dinghua Shi , Xiang Zhu , Liming Liu

We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…

Probability · Mathematics 2007-05-23 Anna Rudas , Balint Toth , Benedek Valko

This paper expands the degree-based consideration of the preferential attachment growth process and applies five different connectivity criteria (node degree, clustering coefficient, betweenness centrality, closeness centrality, and…

Physics and Society · Physics 2020-01-16 Dimitrios Tsiotas

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…

Statistical Mechanics · Physics 2009-10-31 P. L. Krapivsky , S. Redner

Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their…

Physics and Society · Physics 2015-05-19 Claudio J. Tessone , Markus M. Geipel , F. Schweitzer

Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree…

Probability · Mathematics 2018-08-07 Tiandong Wang , Sidney I. Resnick

We consider a simple Preferential Attachment graph process, which begins with a finite graph, and in which a new $(t+1)$st vertex is added at each subsequent time step $t$, and connected to each previous vertex $u \leq t$ with probability…

Combinatorics · Mathematics 2020-04-22 Richard Elwes

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…

Probability · Mathematics 2018-12-27 Tomasz Luczak , Abram Magner , Wojciech Szpankowski

Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as…

Physics and Society · Physics 2013-05-30 Luca Ferretti , Michele Cortelezzi , Bin Yang , Giacomo Marmorini , Ginestra Bianconi

Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive…

Physics and Society · Physics 2016-03-08 I. Sendiña-Nadal , M. M. Danziger , Z. Wang , S. Havlin , S. Boccaletti

We analyze growing networks that are built by enhanced redirection. Nodes are sequentially added and each incoming node attaches to a randomly chosen 'target' node with probability 1-r, or to the parent of the target node with probability…

Statistical Mechanics · Physics 2014-07-25 Alan Gabel , P. L. Krapivsky , S. Redner

We study a generalization of the affine preferential attachment model where triangles are randomly added to the graph. We show that the model exhibits an asymptotically power-law degree distribution with adjustable parameter $\gamma\in…

Probability · Mathematics 2025-04-04 Angelica Pachon , Robin Stephenson

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…

Probability · Mathematics 2015-03-18 Emmanuel Jacob , Peter Mörters

We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree $\kappa $. Using very simple rules for forming such preferred degree networks, we find…

Statistical Mechanics · Physics 2012-12-05 Shivakumar Jolad , Wenjia Liu , B. Schmittmann , R. K. P. Zia

We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are…

Statistical Mechanics · Physics 2026-02-03 Harrison Hartle , P. L. Krapivsky

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.…

Disordered Systems and Neural Networks · Physics 2008-12-30 Shai Carmi , P. L. Krapivsky , Daniel ben-Avraham