scholarly journals Clustering in a hyperbolic model of complex networks

2021 ◽  
Vol 26 (0) ◽  
Author(s):  
Nikolaos Fountoulakis ◽  
Pim van der Hoorn ◽  
Tobias Müller ◽  
Markus Schepers
Keyword(s):  
Complex Networks ◽  
Hyperbolic Model

scholarly journals The probability of connectivity in a hyperbolic model of complex networks

2016 ◽  
Vol 49 (1) ◽  
pp. 65-94 ◽  
Author(s):  
Michel Bode ◽  
Nikolaos Fountoulakis ◽  
Tobias Müller
Keyword(s):  
Complex Networks ◽  
Hyperbolic Model ◽  
Probability Of Connectivity

scholarly journals On the Largest Component of a Hyperbolic Model of Complex Networks

10.37236/4958 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Michel Bode ◽  
Nikolaos Fountoulakis ◽  
Tobias Müller
Keyword(s):  
Complex Networks ◽  
Uniform Distribution ◽  
Random Graph ◽  
Power Law ◽  
High Probability ◽  
Degree Sequence ◽  
Hyperbolic Model ◽  
Hyperbolic Distance ◽  
Component Structure ◽  
Two Parameters

We consider a model for complex networks that was introduced by Krioukov et al.  In this model, $N$ points are chosen randomly inside a disk on the hyperbolic plane and any two of them are joined by an  edge if they are within a certain hyperbolic distance.  The $N$ points are distributed according to a quasi-uniform distribution, which is a distorted version of  the uniform distribution. The model turns out to behave similarly to the well-known Chung-Lu model, but without the independence between the edges. Namely, it exhibits a power-law degree sequence and small distances but, unlike the Chung-Lu model and many other well-known models for complex networks, it also exhibits clustering. The model is controlled by two parameters $\alpha$ and $\nu$ where, roughly speaking, $\alpha$ controls the exponent of the power-law and $\nu$ controls the average degree. The present paper focuses on the evolution of the component structure of the random graph.  We show that (a) for $\alpha > 1$ and $\nu$ arbitrary, with high probability, as the number of vertices grows, the largest component of the random graph has sublinear order; (b) for $\alpha < 1$ and $\nu$ arbitrary with high probability there is a "giant" component  of linear order,  and (c) when $\alpha=1$ then there is a non-trivial phase transition for the existence of a linear-sized component in terms of $\nu$. A corrigendum was added to this paper 29 Dec 2018.

Complex Networks

2009 ◽  
Author(s):  
Reuven Cohen ◽  
Shlomo Havlin
Keyword(s):  
Complex Networks

Complex Networks from Simple Rules

2013 ◽  
Vol 22 (2) ◽  
pp. 151-174 ◽  
Author(s):  
Richard Southwell ◽  
Jianwei Huang ◽  
Chris Cannings ◽  
◽  
Keyword(s):  
Complex Networks ◽  
Simple Rules

Algorithm for detecting module structure in complex networks based on node type

2009 ◽  
Vol 28 (10) ◽  
pp. 2590-2593
Author(s):  
Wei SHI ◽  
Zheng ZHAO ◽  
Gui-xiang XUE
Keyword(s):  
Complex Networks ◽  
Module Structure ◽  
Node Type
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