scholarly journals Finding Induced Subgraphs in Scale-Free Inhomogeneous Random Graphs

2018 ◽  
pp. 1-15
Author(s):  
Ellen Cardinaels ◽  
Johan S. H. van Leeuwaarden ◽  
Clara Stegehuis
Keyword(s):  
Random Graphs ◽  
Induced Subgraphs ◽  
Scale Free ◽  
Inhomogeneous Random Graphs

scholarly journals Counting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs

2019 ◽  
Vol 175 (1) ◽  
pp. 161-184
Author(s):  
A. J. E. M. Janssen ◽  
Johan S. H. van Leeuwaarden ◽  
Seva Shneer
Keyword(s):  
Random Graphs ◽  
Scale Free ◽  
Inhomogeneous Random Graphs

scholarly journals Large Holes in Quasi-Random Graphs

10.37236/784 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Joanna Polcyn
Keyword(s):  
Random Graphs ◽  
Induced Subgraphs ◽  
Degree Condition ◽  
Almost All

Quasi-random graphs have the property that the densities of almost all pairs of large subsets of vertices are similar, and therefore we cannot expect too large empty or complete bipartite induced subgraphs in these graphs. In this paper we answer the question what is the largest possible size of such subgraphs. As an application, a degree condition that guarantees the connection by short paths in quasi-random pairs is stated.

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 Big Jobs Arrive Early: From Critical Queues to Random Graphs

2020 ◽  
Vol 10 (4) ◽  
pp. 310-334
Author(s):  
Gianmarco Bet ◽  
Remco van der Hofstad ◽  
Johan S. H. van Leeuwaarden
Keyword(s):  
Head Start ◽  
Random Graphs ◽  
Queue Length ◽  
Busy Period ◽  
Asymptotic Result ◽  
Service Requirement ◽  
Exploration Process ◽  
Asymptotic Regime ◽  
Long Period ◽  
Inhomogeneous Random Graphs

We consider a queue to which only a finite pool of n customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement S arrives to the queue after an exponentially distributed time with mean S-α for some [Formula: see text]; therefore, larger service requirements trigger customers to join earlier. This finite-pool queue interpolates between two previously studied cases: α = 0 gives the so-called [Formula: see text] queue and α = 1 is closely related to the exploration process for inhomogeneous random graphs. We consider the asymptotic regime in which the pool size n grows to infinity and establish that the scaled queue-length process converges to a diffusion process with a negative quadratic drift. We leverage this asymptotic result to characterize the head start that is needed to create a long period of activity. We also describe how this first busy period of the queue gives rise to a critically connected random forest.

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

On Random Intersection Graphs: The Subgraph Problem

1999 ◽  
Vol 8 (1-2) ◽  
pp. 131-159 ◽  
Author(s):  
MICHAŁ KAROŃSKI ◽  
EDWARD R. SCHEINERMAN ◽  
KAREN B. SINGER-COHEN
Keyword(s):  
Circuit Design ◽  
Random Graphs ◽  
Induced Subgraphs ◽  
Intersection Graphs ◽  
New Model ◽  
Gate Matrix

A new model of random graphs – random intersection graphs – is introduced. In this model, vertices are assigned random subsets of a given set. Two vertices are adjacent provided their assigned sets intersect. We explore the evolution of random intersection graphs by studying thresholds for the appearance and disappearance of small induced subgraphs. An application to gate matrix circuit design is presented.

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