Range-based attack on links in scale-free networks: Are long-range links responsible for the small-world phenomenon?

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

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Distances in scale-free networks: the ultra small world

Complex Networks ◽

10.1017/cbo9780511780356.006 ◽

2013 ◽

pp. 65-80

Author(s):

Reuven Cohen ◽

Shlomo Havlin

Keyword(s):

Small World ◽

Scale Free ◽

Scale Free Networks

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EXPRESS PASSENGER TRANSPORT SYSTEM AS A SCALE-FREE NETWORK

Modern Physics Letters B ◽

10.1142/s0217984906011803 ◽

2006 ◽

Vol 20 (27) ◽

pp. 1755-1761 ◽

Cited By ~ 8

Author(s):

BAIBAI FU ◽

ZIYOU GAO ◽

FASHENG LIU ◽

XIANJUAN KONG

Keyword(s):

Transport System ◽

Network Topology ◽

Small World ◽

Power Exponent ◽

Scale Free Network ◽

Passenger Transport ◽

Scale Free ◽

Scale Free Networks ◽

Highway Network ◽

Free Network

An express highway itself is not a scale-free network, while the Express Passenger Transport System (EPTS) on the express highway network has the properties of a small-world and scale-free network. Data analysis based on the observation of the EPTS in Shandong province, China, shows that the EPTS has the properties of scale-free networks and the power exponent λ of the distribution is equal to about 2.1. Based on the scale-free network topology structure of the EPTS network, the construction of the EPTS network will be more efficient and robust.

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Network rewiring dynamics with convergence towards a star network

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2016.0236 ◽

2016 ◽

Vol 472 (2194) ◽

pp. 20160236 ◽

Cited By ~ 1

Author(s):

P. A. Whigham ◽

G. Dick ◽

M. Parry

Keyword(s):

Infectious Disease ◽

Random Network ◽

Small World ◽

Fixation Time ◽

Fixed Size ◽

Star Network ◽

Scale Free ◽

Link Type ◽

Scale Free Networks ◽

Network Rewiring

Network rewiring as a method for producing a range of structures was first introduced in 1998 by Watts & Strogatz ( Nature 393 , 440–442. ( doi:10.1038/30918 )). This approach allowed a transition from regular through small-world to a random network. The subsequent interest in scale-free networks motivated a number of methods for developing rewiring approaches that converged to scale-free networks. This paper presents a rewiring algorithm (RtoS) for undirected, non-degenerate, fixed size networks that transitions from regular, through small-world and scale-free to star-like networks. Applications of the approach to models for the spread of infectious disease and fixation time for a simple genetics model are used to demonstrate the efficacy and application of the approach.

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Propagation and stability in software: A complex network perspective

International Journal of Modern Physics C ◽

10.1142/s0129183115500527 ◽

2015 ◽

Vol 26 (05) ◽

pp. 1550052 ◽

Cited By ~ 6

Author(s):

Lei Wang ◽

Ping Wang

Keyword(s):

Software Engineering ◽

Complex Networks ◽

Large Scale ◽

Structural Difference ◽

Small World ◽

Change Propagation ◽

Small World Networks ◽

Typical Structure ◽

Scale Free ◽

Scale Free Networks

In this paper, we attempt to understand the propagation and stability feature of large-scale complex software from the perspective of complex networks. Specifically, we introduced the concept of "propagation scope" to investigate the problem of change propagation in complex software. Although many complex software networks exhibit clear "small-world" and "scale-free" features, we found that the propagation scope of complex software networks is much lower than that of small-world networks and scale-free networks. Furthermore, because the design of complex software always obeys the principles of software engineering, we introduced the concept of "edge instability" to quantify the structural difference among complex software networks, small-world networks and scale-free networks. We discovered that the edge instability distribution of complex software networks is different from that of small-world networks and scale-free networks. We also found a typical structure that contributes to the edge instability distribution of complex software networks. Finally, we uncovered the correlation between propagation scope and edge instability in complex networks by eliminating the edges with different instability ranges.

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Complex networks

10.1093/oxfordhb/9780198744191.013.43 ◽

2018 ◽

Author(s):

Graziano Vernizzi ◽

Henri Orland

Keyword(s):

Complex Networks ◽

Small World ◽

Laplacian Matrix ◽

Square Lattice ◽

Small World Networks ◽

Scale Free ◽

Scale Free Networks ◽

Free Network ◽

Scale Free Graphs ◽

Regular Networks

This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how it can be applied to calculate the spectral densities of the adjacency matrix and Laplacian matrix of a scale free network. It then shows how the effective medium approximation can be used to treat networks with finite mean degree and concludes with a discussion of the local properties of random matrices associated with complex networks.

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Scale-free networks which are highly assortative but not small world

Physical Review E ◽

10.1103/physreve.77.066112 ◽

2008 ◽

Vol 77 (6) ◽

Cited By ~ 31

Author(s):

Michael Small ◽

Xiaoke Xu ◽

Jin Zhou ◽

Jie Zhang ◽

Junfeng Sun ◽

...

Keyword(s):

Small World ◽

Scale Free ◽

Scale Free Networks

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Resilience of Interbank Market Networks to Shocks

Discrete Dynamics in Nature and Society ◽

10.1155/2011/594945 ◽

2011 ◽

Vol 2011 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Shouwei Li ◽

Jianmin He

Keyword(s):

Network Models ◽

Small World ◽

Interbank Market ◽

Small World Networks ◽

Scale Free ◽

Scale Free Networks ◽

Tiered Networks ◽

The Stability ◽

Random Shocks ◽

Market Networks

This paper first constructs a tiered network model of the interbank market. Then, from the perspective of contagion risk, it studies numerically the resilience of four types of interbank market network models to shocks, namely, tiered networks, random networks, small-world networks, and scale-free networks. This paper studies the interbank market with homogeneous and heterogeneous banks and analyzes random shocks and selective shocks. The study reveals that tiered interbank market networks and random interbank market networks are basically more vulnerable against selective shocks, while small-world interbank market networks and scale-free interbank market networks are generally more vulnerable against random shocks. Besides, the results indicate that, in the four types of interbank market networks, scale-free networks have the highest stability against shocks, while small-world networks are the most vulnerable. When banks are homogeneous, faced with selective shocks, the stability of the tiered interbank market networks is slightly lower than that of random interbank market networks, whereas, in other cases, the stability of the tiered interbank market networks is basically between that of random interbank market networks and that of scale-free interbank market networks.

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Asynchronous discussion groups as Small World and Scale Free Networks

First Monday ◽

10.5210/fm.v9i9.1170 ◽

2004 ◽

Vol 9 (9) ◽

Cited By ~ 19

Author(s):

Gilad Ravid ◽

Sheizaf Rafaeli

Keyword(s):

Small World ◽

Discussion Groups ◽

Asynchronous Discussion ◽

Scale Free ◽

Scale Free Networks ◽

Asynchronous Discussion Groups

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Organizational and Formational Structures of Networks in the Mental Lexicon: A State-Of-The-Art through Systematic Review

Languages ◽

10.3390/languages5010001 ◽

2019 ◽

Vol 5 (1) ◽

pp. 1

Author(s):

Luke McCarthy ◽

Imma Miralpeix

Keyword(s):

Systematic Review ◽

State Of The Art ◽

Mental Lexicon ◽

Small World ◽

Structural Features ◽

Future Research ◽

Emergent Properties ◽

Scale Free ◽

Scale Free Networks ◽

Network Patterns

This state-of-the-art presents a systematic exploration on the use of network patterns in global research efforts to understand, organize and represent the mental lexicon. Results have shown an increase over recent years in the usage of complex, small-world and scale-free network patterns within the literature. With the increasing complexity of network patterns, we see more potential in the inter-disciplinary exploration of the mental lexicon through universal and mathematically-describable, behavioral patterns in small-world and scale-free networks. A systematic review of 36 items of methodologically-selected literature serve as a means to explore how the greater literary body understands network structures within the mental lexicon. Network-based approaches are discriminated between three contrasting varieties. These include: ‘simple networks’, characterized by arbitrarily organized graph patterns of metaphorical importance; ‘connectionist networks’, a broad category of networks which explore the structural features of a system through the analysis of emergent properties; and lastly ‘complex networks’, distinguished as small-world, scale-free networks which follow a strict and mathematically-describable structure in agreement with the Barabási–Albert model. Each network approach is explored in terms of their discernible differences which relate to their parameters and affect their implications. A final evaluation of observed patterns within the selected literature is offered, as well as an elaboration on the sense of trajectory beheld in the research in order to offer insight and orientation for future research.

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