scholarly journals PageRank in Scale-Free Random Graphs

2014 ◽  
pp. 120-131 ◽  
Author(s):  
Ningyuan Chen ◽  
Nelly Litvak ◽  
Mariana Olvera-Cravioto
Keyword(s):  
Random Graphs ◽  
Scale Free

scholarly journals Robustness and Vulnerability of Scale-Free Random Graphs

2004 ◽  
Vol 1 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Béla Bollobás ◽  
Oliver Riordan
Keyword(s):  
Random Graphs ◽  
Scale Free

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 Diameter in ultra‐small scale‐free random graphs

2018 ◽  
Vol 54 (3) ◽  
pp. 444-498 ◽  
Author(s):  
Francesco Caravenna ◽  
Alessandro Garavaglia ◽  
Remco van der Hofstad
Keyword(s):  
Random Graphs ◽  
Small Scale ◽  
Scale Free

scholarly journals Scale-free network clustering in hyperbolic and other random graphs

2019 ◽  
Vol 52 (29) ◽  
pp. 295101 ◽  
Author(s):  
Clara Stegehuis ◽  
Remco van der Hofstad ◽  
Johan S H van Leeuwaarden
Keyword(s):  
Random Graphs ◽  
Network Clustering ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

scholarly journals Unimodular lattice triangulations as small-world and scale-free random graphs

2015 ◽  
Vol 17 (2) ◽  
pp. 023013 ◽  
Author(s):  
B Krüger ◽  
E M Schmidt ◽  
K Mecke
Keyword(s):  
Random Graphs ◽  
Small World ◽  
Unimodular Lattice ◽  
Scale Free

scholarly journals The degree sequences and spectra of scale-free random graphs

2006 ◽  
Vol 29 (2) ◽  
pp. 226-242 ◽  
Author(s):  
Jonathan Jordan
Keyword(s):  
Random Graphs ◽  
Degree Sequences ◽  
Scale Free

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 Erdos – Renyi Random Graph and Machine Learning Based Botnet Detection

2020 ◽  
Vol 9 (5) ◽  
pp. 1037-1040
Keyword(s):  
Machine Learning ◽  
Probability Theory ◽  
Graph Theory ◽  
Complex Network ◽  
Random Graphs ◽  
Connected Graph ◽  
Free Graph ◽  
Botnet Detection ◽  
Scale Free ◽  
Made In

Basically large networks are prone to attacks by bots and lead to complexity. When the complexity occurs then it is difficult to overcome the vulnerability in the network connections. In such a case, the complex network could be dealt with the help of probability theory and graph theory concepts like Erdos – Renyi random graphs, Scale free graph, highly connected graph sequences and so on. In this paper, Botnet detection using Erdos – Renyi random graphs whose patterns are recognized as the number of connections that the vertices and edges made in the network is proposed. This paper also presents the botnet detection concepts based on machine learning.

scholarly journals Local Degree Distribution in Scale Free Random Graphs

2011 ◽  
Vol 16 (0) ◽  
pp. 1465-1488 ◽  
Author(s):  
Agnes Backhausz ◽  
Tamas Mori
Keyword(s):  
Random Graphs ◽  
Degree Distribution ◽  
Scale Free ◽  
Local Degree
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