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.

THE SCALE-FREE AND SMALL-WORLD PROPERTIES OF COMPLEX NETWORKS ON SIERPINSKI-TYPE HEXAGON

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050054
Author(s):  
KUN CHENG ◽  
DIRONG CHEN ◽  
YUMEI XUE ◽  
QIAN ZHANG
Keyword(s):  
Power Law ◽  
Path Length ◽  
Small World ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Scale Free ◽  
Power Law Exponent ◽  
Self Similar ◽  
Encoding Method

In this paper, a network is generated from a Sierpinski-type hexagon by applying the encoding method in fractal. The criterion of neighbor is established to quantify the relationships among the nodes in the network. Based on the self-similar structures, we verify the scale-free and small-world effects. The power-law exponent on degree distribution is derived to be [Formula: see text] and the average clustering coefficients are shown to be larger than [Formula: see text]. Moreover, we give the bounds of the average path length of our proposed network from the renewal theorem and self-similarity.

scholarly journals Observational evidence in favor of scale-free evolution of sunspot groups

2018 ◽  
Vol 618 ◽  
pp. A183
Author(s):  
A. Shapoval ◽  
J.-L. Le Mouël ◽  
M. Shnirman ◽  
V. Courtillot
Keyword(s):  
Weibull Distribution ◽  
Power Law ◽  
Large Range ◽  
Scale Free ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Spatio Temporal ◽  
Computational Procedures ◽  
Definition Of ◽  
Sunspot Groups

Context. The hypothesis stating that the distribution of sunspot groups versus their size (φ) follows a power law in the domain of small groups was recently highlighted but rejected in favor of a Weibull distribution. Aims. In this paper we reconsider this question, and are led to the opposite conclusion. Methods. We have suggested a new definition of group size, namely the spatio-temporal “volume” (V) obtained as the sum of the observed daily areas instead of a single area associated with each group. Results. With this new definition of “size”, the width of the power-law part of the distribution φ ∼ 1/Vβ increases from 1.5 to 2.5 orders of magnitude. The exponent β is close to 1. The width of the power-law part and its exponent are stable with respect to the different catalogs and computational procedures used to reduce errors in the data. The observed distribution is not fit adequately by a Weibull distribution. Conclusions. The existence of a wide 1/V part of the distribution φ suggests that self-organized criticality underlies the generation and evolution of sunspot groups and that the mechanism responsible for it is scale-free over a large range of sizes.

scholarly journals Scale-free networks with the power-law exponent between 1 and 3

2007 ◽  
Vol 56 (10) ◽  
pp. 5635
Author(s):  
Guo Jin-Li ◽  
Wang Li-Na
Keyword(s):  
Power Law ◽  
Scale Free ◽  
Power Law Exponent ◽  
Scale Free Networks

Epidemic spreading on evolving networks

2019 ◽  
Vol 33 (23) ◽  
pp. 1950266 ◽  
Author(s):  
Jin-Xuan Yang
Keyword(s):  
Preferential Attachment ◽  
Small World ◽  
Network Evolution ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Scale Free ◽  
Evolving Networks ◽  
Power Law Exponent ◽  
Free Network ◽  
Over Time

Network structure will evolve over time, which will lead to changes in the spread of the epidemic. In this work, a network evolution model based on the principle of preferential attachment is proposed. The network will evolve into a scale-free network with a power-law exponent between 2 and 3 by our model, where the exponent is determined by the evolution parameters. We analyze the epidemic spreading process as the network evolves from a small-world one to a scale-free one, including the changes in epidemic threshold over time. The condition of epidemic threshold to increase is given with the evolution processes. The simulated results of real-world networks and synthetic networks show that as the network evolves at a low evolution rate, it is more conducive to preventing epidemic spreading.

Infection Dynamics on Growing Networks

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4045-4061 ◽  
Author(s):  
Ying-Cheng Lai ◽  
Zonghua Liu ◽  
Nong Ye
Keyword(s):  
Heterogeneous Networks ◽  
Network Architecture ◽  
Nonlinear Differential Equations ◽  
Small World ◽  
Science And Engineering ◽  
Scale Free ◽  
Infection Dynamics ◽  
Growing Networks ◽  
Spread Of Infection ◽  
Heuristic Analysis

We consider the entire spectrum of architectures for large, growing, and complex networks, ranging from being heterogeneous (scale-free) to homogeneous (random or small-world), and investigate the infection dynamics by using a realistic three-state epidemiological model. In this framework, a node can be in one of the three states: susceptible (S), infected (I), or refractory (R), and the populations in the three groups are approximately described by a set of nonlinear differential equations. Our heuristic analysis predicts that, (1) regardless of the network architecture, there exists a substantial fraction of nodes that can never be infected, and (2) heterogeneous networks are relatively more robust against spread of infection as compared with homogeneous networks. These are confirmed numerically. We have also considered the problem of deliberate immunization for preventing wide spread of infection, with the result that targeted immunization can be quite effective for heterogeneous networks. We believe these results are important for a host of problems in many areas of natural science and engineering, and in social sciences as well.

Dynamic Key Distribution Scheme Based on Complex Network Synchronization

2013 ◽  
Vol 427-429 ◽  
pp. 2329-2332
Author(s):  
Ying Liu
Keyword(s):  
Complex Network ◽  
Low Cost ◽  
Small World ◽  
Key Distribution ◽  
Necessary Condition ◽  
Scale Free ◽  
Self Organized ◽  
Distribution Scheme ◽  
Defects Analysis ◽  
Dynamic Key

As a low-consumption, low-cost, distributed self-organized network, wireless sensor network communicates as a self-similar, small-world and scale-free complex network. Based on the defects analysis of digital communication and sufficient necessary condition of analog signal synchronization, we proposed a novel key distribution scheme in this paper. While some performance analyses as well as some prospects are also given in the end.

A Small-World Model of Scale-Free Networks: Features and Verifications

2011 ◽  
Vol 50-51 ◽  
pp. 166-170 ◽  
Author(s):  
Wen Jun Xiao ◽  
Shi Zhong Jiang ◽  
Guan Rong Chen
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Sequence ◽  
Small World ◽  
Static Condition ◽  
Vertex Degree ◽  
Power Law Distribution ◽  
Least Common Multiple ◽  
Scale Free ◽  
Vertex Degrees

It is now well known that many large-sized complex networks obey a scale-free power-law vertex-degree distribution. Here, we show that when the vertex degrees of a large-sized network follow a scale-free power-law distribution with exponent  2, the number of degree-1 vertices, if nonzero, is of order N and the average degree is of order lower than log N, where N is the size of the network. Furthermore, we show that the number of degree-1 vertices is divisible by the least common multiple of , , . . ., , and l is less than log N, where l = < is the vertex-degree sequence of the network. The method we developed here relies only on a static condition, which can be easily verified, and we have verified it by a large number of real complex networks.

ERRATA: FERMIONIC AND BOSONIC SELF-ORGANIZED NETWORKS: A REPRESENTATION OF QUANTUM STATISTICS

2001 ◽  
Vol 15 (03) ◽  
pp. 313-320 ◽  
Author(s):  
GINESTRA BIANCONI
Keyword(s):  
Cayley Tree ◽  
Self Organization ◽  
High Tc Superconductors ◽  
Quantum Distribution ◽  
High Tc ◽  
Scale Free ◽  
New Class ◽  
Self Organized ◽  
The Right ◽  
Quantum Distributions

A new class of self organized networks is described that is relevant to understand the emerging order in a large number of complex systems such as biological systems, the web, and heterogeneous phases in high Tc superconductors. The Bose and Fermi quantum distributions are shown to be the right tool to describe the two extreme limit distributions, the scale-free and the Cayley-tree network respectively. The new class of self-organized networks is described by a 'mixed' quantum distribution. Here the bosonic and fermionic types of self organization coexists, maintaining the same 'ergodic' nature.

scholarly journals Self-Organizing Networks in Complex Infrastructure Projects

2018 ◽  
Vol 49 (2) ◽  
pp. 18-41 ◽  
Author(s):  
Stephen Pryke ◽  
Sulafa Badi ◽  
Huda Almadhoob ◽  
Balamurugan Soundararaj ◽  
Simon Addyman
Keyword(s):  
Network Theory ◽  
Small World ◽  
Self Organization ◽  
Infrastructure Projects ◽  
Self Organized ◽  
Management Techniques ◽  
Path Lengths ◽  
High Degree ◽  
Self Organizing Networks ◽  
Self Organizing

While significant importance is given to establishing formal organizational and contractual hierarchies, existing project management techniques neglect the management of self-organizing networks in large-infrastructure projects. We offer a case-specific illustration of self-organization using network theory as an investigative lens. The findings have shown that these networks exhibit a high degree of sparseness, short path lengths, and clustering in dense “functional” communities around highly connected actors, thus demonstrating the small-world topology observed in diverse real-world self-organized networks. The study underlines the need for these non-contractual functions and roles to be identified and sponsored, allowing the self-organizing network the space and capacity to evolve.

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