Deterministic small-world graphs and the eigenvalue power law of Internet

2004 ◽  
Author(s):  
F. Cornelias ◽  
S. Gago
Keyword(s):  
Power Law ◽  
Small World ◽  
Small World Graphs

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

scholarly journals Sublinear domination and core–periphery networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marios Papachristou
Keyword(s):  
Network Model ◽  
Power Law ◽  
Real World ◽  
Random Network ◽  
Small World ◽  
The Core ◽  
Entire Network

AbstractIn this paper we devise a generative random network model with core–periphery properties whose core nodes act as sublinear dominators, that is, if the network has n nodes, the core has size o(n) and dominates the entire network. We show that instances generated by this model exhibit power law degree distributions, and incorporates small-world phenomena. We also fit our model in a variety of real-world networks.

Efficient and Robust WiFi Indoor Positioning Using Hierarchical Navigable Small World Graphs

2018 ◽  
Author(s):  
Max Willian Soares Lima ◽  
Horacio A. B. Fernandes de Oliveira ◽  
Eulanda Miranda dos Santos ◽  
Edleno Silva de Moura ◽  
Rafael Kohler Costa ◽  
...  
Keyword(s):  
Small World ◽  
Indoor Positioning ◽  
Small World Graphs

scholarly journals Models And Mining Of On-Line Social Networks

2021 ◽  
Author(s):  
Yanhua Tian
Keyword(s):  
Social Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Small World ◽  
Spectral Expansion ◽  
On Line ◽  
Simulation Results ◽  
Small World Property ◽  
P Type ◽  
Law Degree

Power law degree distribution, the small world property, and bad spectral expansion are three of the most important properties of On-line Social Networks (OSNs). We sampled YouTube and Wikipedia to investigate OSNs. Our simulation and computational results support the conclusion that OSNs follow a power law degree distribution, have the small world property, and bad spectral expansion. We calculated the diameters and spectral gaps of OSNs samples, and compared these to graphs generated by the GEO-P model. Our simulation results support the Logarithmic Dimension Hypothesis, which conjectures that the dimension of OSNs is m = [log N]. We introduced six GEO-P type models. We ran simulations of these GEO-P-type models, and compared the simulated graphs with real OSN data. Our simulation results suggest that, except for the GEO-P (GnpDeg) model, all our models generate graphs with power law degree distributions, the small world property, and bad spectral expansion.

scholarly journals Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Géza Ódor ◽  
Jeffrey Kelling
Keyword(s):  
Control Parameter ◽  
Mean Field ◽  
Small World ◽  
Kuramoto Model ◽  
Crossover Point ◽  
Small World Graphs ◽  
Synchronization Phase ◽  
Experimental Values ◽  
The Kuramoto Model ◽  
Parameter Dependent

AbstractThe hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d < 4, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law–tailed synchronization durations, with τt ≃ 1.2(1), away from experimental values for the brain. For comparison, on a large two-dimensional lattice, having additional random, long-range links, we obtain a mean-field value: τt ≃ 1.6(1). However, below the transition of the connectome we found global coupling control-parameter dependent exponents 1 < τt ≤ 2, overlapping with the range of human brain experiments. We also studied the effects of random flipping of a small portion of link weights, mimicking a network with inhibitory interactions, and found similar results. The control-parameter dependent exponent suggests extended dynamical criticality below the transition point.

Centrality Based Visualization of Small World Graphs

2008 ◽  
Vol 27 (3) ◽  
pp. 975-982 ◽  
Author(s):  
F. van Ham ◽  
M. Wattenberg
Keyword(s):  
Small World ◽  
Small World Graphs

SELF-ORGANIZED CORONA GRAPHS: A DETERMINISTIC COMPLEX NETWORK MODEL WITH HIERARCHICAL STRUCTURE

2019 ◽  
Vol 22 (06) ◽  
pp. 1950019
Author(s):  
ROHAN SHARMA ◽  
BIBHAS ADHIKARI ◽  
TYLL KRUEGER
Keyword(s):  
Power Law ◽  
Small World ◽  
Self Organization ◽  
Scale Free ◽  
Self Organized ◽  
Power Law Exponent ◽  
Growing Networks ◽  
Growing Network ◽  
Hierarchical Pattern ◽  
Corona Graphs

In this paper, we propose a self-organization mechanism for newly appeared nodes during the formation of corona graphs that define a hierarchical pattern in the resulting corona graphs and we call it self-organized corona graphs (SoCG). We show that the degree distribution of SoCG follows power-law in its tail with power-law exponent approximately 2. We also show that the diameter is less equal to 4 for SoCG defined by any seed graph and for certain seed graphs, the diameter remains constant during its formation. We derive lower bounds of clustering coefficients of SoCG defined by certain seed graphs. Thus, the proposed SoCG can be considered as a growing network generative model which is defined by using the corona graphs and a self-organization process such that the resulting graphs are scale-free small-world highly clustered growing networks. The SoCG defined by a seed graph can also be considered as a network with a desired motif which is the seed graph itself.

scholarly journals Small world graphs by iterated local edge formation

2005 ◽  
Vol 71 (4) ◽  
Author(s):  
Ph. Blanchard ◽  
T. Krueger ◽  
A. Ruschhaupt
Keyword(s):  
Small World ◽  
Small World Graphs ◽  
Local Edge
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