scholarly journals Greedy routing in small-world networks with power-law degrees

2014 ◽  
Vol 27 (4) ◽  
pp. 231-253 ◽  
Author(s):  
Pierre Fraigniaud ◽  
George Giakkoupis
Keyword(s):  
Power Law ◽  
Small World ◽  
Greedy Routing ◽  
Small World Networks

scholarly journals Multistage Random Growing Small-World Networks with Power-Law Degree Distribution

2006 ◽  
Vol 23 (3) ◽  
pp. 746-749 ◽  
Author(s):  
Liu Jian-Guo ◽  
Dang Yan-Zhong ◽  
Wang Zhong-Tuo
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Small World ◽  
Small World Networks ◽  
Law Degree

MODELING THE TOPOLOGY OF SDH NETWORKS

2008 ◽  
Vol 19 (12) ◽  
pp. 1809-1820 ◽  
Author(s):  
A. SANTIAGO ◽  
J. P. CÁRDENAS ◽  
M. L. MOURONTE ◽  
V. FELIU ◽  
R. M. BENITO
Keyword(s):  
Optical Networks ◽  
Power Law ◽  
Ad Hoc ◽  
Small World ◽  
The Internet ◽  
Topological Properties ◽  
Small World Networks ◽  
Synchronous Digital Hierarchy ◽  
Worldwide Web ◽  
Real Complex

SDH (Synchronous Digital Hierarchy) is the standard technology for the information transmission in broadband optical networks. Unlike the Internet, SDH networks are strictly planned; rings, meshes, stars, or tree-branches topologies are designed to connect their basic elements. In spite of that, we have found that the SDH network operated by Telefónica in Spain shares remarkable topological properties with other real complex networks empirically analyzed, such as the worldwide web network. In particular, we have found power-law scaling in the degree distribution (P(k) ~ k-γ) and properties of small world networks. Considering real planning directives that take into account geographical and technological variables, we propose an ad hoc computational model that reproduces the aforementioned topological traits observed in the Spanish SDH network.

scholarly journals Kleinberg Navigation on Anisotropic Lattices

2008 ◽  
Vol 2008 ◽  
pp. 1-4 ◽  
Author(s):  
J. M. Campuzano ◽  
J. P. Bagrow ◽  
D. ben-Avraham
Keyword(s):  
Long Range ◽  
Power Law ◽  
Finite Size ◽  
Small World ◽  
Small World Networks ◽  
Infinite Lattice ◽  
Preferred Direction ◽  
Lattice Size ◽  
Anisotropic Lattices ◽  
Anisotropy Strength

We study the Kleinberg problem of navigation in small-world networks when the underlying lattice is stretched along a preferred direction. Extensive simulations confirm that maximally efficient navigation is attained when the length r of long-range links is taken from the distribution P(r)∼r−α, when the exponent α is equal to 2, the dimension of the underlying lattice, regardless of the amount of anisotropy, but only in the limit of infinite lattice size, L→∞. For finite size lattices we find an optimal α(L) that depends strongly on L. The convergence to α=2 as L→∞ shows interesting power-law dependence on the anisotropy strength.

Processes on annealed and quenched power-law small-world networks

2005 ◽  
Author(s):  
Balazs Kozma ◽  
Matthew B. Hastings ◽  
Gyorgy Korniss
Keyword(s):  
Power Law ◽  
Small World ◽  
Small World Networks

scholarly journals Diffusion Processes on Power-Law Small-World Networks

2005 ◽  
Vol 95 (1) ◽  
Author(s):  
Balázs Kozma ◽  
Matthew B. Hastings ◽  
G. Korniss
Keyword(s):  
Power Law ◽  
Diffusion Processes ◽  
Small World ◽  
Small World Networks

Networks

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Phase Diagrams ◽  
Community Detection ◽  
Network Science ◽  
Small World ◽  
Small World Networks ◽  
Multilayer Networks ◽  
Basic Vocabulary

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

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.

scholarly journals Multifractal analysis of eigenvectors of small-world networks

2021 ◽  
Vol 144 ◽  
pp. 110745
Author(s):  
Ankit Mishra ◽  
Jayendra N. Bandyopadhyay ◽  
Sarika Jalan
Keyword(s):  
Multifractal Analysis ◽  
Small World ◽  
Small World Networks
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