6. Random Graphs, Small-Worlds and Scale-Free Networks

2005 ◽  
pp. 57-76 ◽  
Author(s):  
Katharina Anna Lehmann ◽  
Michael Kaufmann
Keyword(s):  
Random Graphs ◽  
Small Worlds ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals Optimal shattering of complex networks

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Nicole Balashov ◽  
Reuven Cohen ◽  
Avieli Haber ◽  
Michael Krivelevich ◽  
Simi Haber
Keyword(s):  
Complex Networks ◽  
Random Graphs ◽  
Polynomial Time ◽  
Optimal Performance ◽  
Regular Graphs ◽  
Scale Free ◽  
Scale Free Networks ◽  
Minimum Number

Abstract We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size.We obtain bounds for different regimes of random regular graphs, Erdős-Rényi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality.Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.

scholarly journals A process of rumour scotching on finite populations

2015 ◽  
Vol 2 (9) ◽  
pp. 150240 ◽  
Author(s):  
Guilherme Ferraz de Arruda ◽  
Elcio Lebensztayn ◽  
Francisco A. Rodrigues ◽  
Pablo Martín Rodríguez
Keyword(s):  
Monte Carlo ◽  
Random Graphs ◽  
Information Dissemination ◽  
Initial Conditions ◽  
Qualitative Behaviour ◽  
Analytical Treatment ◽  
Scale Free ◽  
Pairwise Interactions ◽  
Scale Free Networks ◽  
Optimal Information

Rumour spreading is a ubiquitous phenomenon in social and technological networks. Traditional models consider that the rumour is propagated by pairwise interactions between spreaders and ignorants. Only spreaders are active and may become stiflers after contacting spreaders or stiflers. Here we propose a competition-like model in which spreaders try to transmit an information, while stiflers are also active and try to scotch it. We study the influence of transmission/scotching rates and initial conditions on the qualitative behaviour of the process. An analytical treatment based on the theory of convergence of density-dependent Markov chains is developed to analyse how the final proportion of ignorants behaves asymptotically in a finite homogeneously mixing population. We perform Monte Carlo simulations in random graphs and scale-free networks and verify that the results obtained for homogeneously mixing populations can be approximated for random graphs, but are not suitable for scale-free networks. Furthermore, regarding the process on a heterogeneous mixing population, we obtain a set of differential equations that describes the time evolution of the probability that an individual is in each state. Our model can also be applied for studying systems in which informed agents try to stop the rumour propagation, or for describing related susceptible–infected–recovered systems. In addition, our results can be considered to develop optimal information dissemination strategies and approaches to control rumour propagation.

scholarly journals Muller’s ratchet in random graphs and scale-free networks

2006 ◽  
Vol 74 (4) ◽  
Author(s):  
Paulo R. A. Campos ◽  
Jaime Combadão ◽  
Francisco Dionisio ◽  
Isabel Gordo
Keyword(s):  
Random Graphs ◽  
Scale Free ◽  
Muller's Ratchet ◽  
Scale Free Networks ◽  
Muller’S Ratchet

scholarly journals Scale-free networks emerging from weighted random graphs

2006 ◽  
Vol 73 (2) ◽  
Author(s):  
Tomer Kalisky ◽  
Sameet Sreenivasan ◽  
Lidia A. Braunstein ◽  
Sergey V. Buldyrev ◽  
Shlomo Havlin ◽  
...  
Keyword(s):  
Random Graphs ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals Dynamics analysis of an online gambling spreading model on scale-free networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yu Kong ◽  
Tao Li ◽  
Yuanmei Wang ◽  
Xinming Cheng ◽  
He Wang ◽  
...  
Keyword(s):  
Network Topology ◽  
Negative Impact ◽  
Online Gambling ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Scale Free ◽  
Spreading Model ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
Gambling Policy

AbstractNowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynamics, a new SHGD (susceptible–hesitator–gambler–disclaimer) online gambling spreading model is proposed on scale-free networks. The spreading dynamics of online gambling is studied. The basic reproductive number $R_{0}$ R 0 is got and analyzed. The basic reproductive number $R_{0}$ R 0 is related to anti-gambling policy and the network topology. Then, gambling-free equilibrium $E_{0}$ E 0 and gambling-prevailing equilibrium $E_{ +} $ E + are obtained. The global stability of $E_{0}$ E 0 is analyzed. The global attractivity of $E_{ +} $ E + and the persistence of online gambling phenomenon are studied. Finally, the theoretical results are verified by some simulations.

scholarly journals Effective gravitation path routing strategy on scale-free networks

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Jinlong Ma ◽  
Junfeng Zhang ◽  
Yongqiang Zhang
Keyword(s):  
Scale Free ◽  
Routing Strategy ◽  
Scale Free Networks
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