scholarly journals Using Spectral Radius Ratio for Node Degree to Analyze the Evolution of Scale-Free Networks and Small-World Networks

2015 ◽  
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Spectral Radius ◽  
Small World ◽  
Radius Ratio ◽  
Node Degree ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks

Propagation and stability in software: A complex network perspective

2015 ◽  
Vol 26 (05) ◽  
pp. 1550052 ◽  
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.

Complex networks

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.

scholarly journals Resilience of Interbank Market Networks to Shocks

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
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.

PERFORMANCE AND ROBUSTNESS OF CELLULAR AUTOMATA COMPUTATION ON IRREGULAR NETWORKS

2007 ◽  
Vol 10 (supp01) ◽  
pp. 85-110 ◽  
Author(s):  
CHRISTIAN DARABOS ◽  
MARIO GIACOBINI ◽  
MARCO TOMASSINI
Keyword(s):  
Information Diffusion ◽  
Small World ◽  
Superior Performance ◽  
Small World Networks ◽  
Scale Free ◽  
Irregular Networks ◽  
Scale Free Networks ◽  
The Face ◽  
Scale Free Graphs ◽  
Synchronization Problems

We investigate the performances of collective task-solving capabilities and the robustness of complex networks of automata using the density and synchronization problems as typical cases. We show by computer simulations that evolved Watts–Strogatz small-world networks have superior performance with respect to several kinds of scale-free graphs. In addition, we show that Watts–Strogatz networks are as robust in the face of random perturbations, both transient and permanent, as configuration scale-free networks, while being widely superior to Barabási–Albert networks. This result differs from information diffusion on scale-free networks, where random faults are highly tolerated by similar topologies.

THE IMPACT OF BANK ACTIVITIES ON CONTAGION RISK IN INTERBANK NETWORKS

2012 ◽  
Vol 15 (supp02) ◽  
pp. 1250086 ◽  
Author(s):  
SHOUWEI LI ◽  
JIANMIN HE
Keyword(s):  
Small World ◽  
Network Structures ◽  
Interbank Market ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Tiered Networks ◽  
Contagion Risk ◽  
The Impact ◽  
Main Factor

In this paper, we investigate how contagion risk is affected by bank activities in four types of interbank network structures, that is, random, small-world, scale-free and tiered networks. We vary the key parameters that define bank activities in the interbank market — including the size of interbank exposures, the size of liquid assets, the heterogeneity of the size of credit lending and the heterogeneity of banks — and analyze the impact of these parameters on contagion risk. First, we find that the size of interbank exposures is the main factor in determining the effect of contagion risk, that increases in the size of interbank exposures may lead to an increase in the threat of contagion risk, that after the size of interbank exposures rises beyond a threshold, the effect of contagion risk in small-world networks is the most significant, followed by that in tiered, random and scale-free networks, respectively. Second, increases in the size of liquid assets can decrease the effect of contagion risk. Third, the impact of the heterogeneity of the size of credit lending on contagion risk varies with interbank network structures. Finally, the effect of contagion risk among heterogeneous banks is stronger than that among homogeneous banks, and there is a positive relationship between the effect of contagion risk and the heterogeneity of banks.

scholarly journals Small-World and Scale-Free Network Models for IoT Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Insoo Sohn
Keyword(s):  
Graph Theory ◽  
Complex Network ◽  
Network Topology ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Massive Number ◽  
Complex Network Models

It is expected that Internet of Things (IoT) revolution will enable new solutions and business for consumers and entrepreneurs by connecting billions of physical world devices with varying capabilities. However, for successful realization of IoT, challenges such as heterogeneous connectivity, ubiquitous coverage, reduced network and device complexity, enhanced power savings, and enhanced resource management have to be solved. All these challenges are heavily impacted by the IoT network topology supported by massive number of connected devices. Small-world networks and scale-free networks are important complex network models with massive number of nodes and have been actively used to study the network topology of brain networks, social networks, and wireless networks. These models, also, have been applied to IoT networks to enhance synchronization, error tolerance, and more. However, due to interdisciplinary nature of the network science, with heavy emphasis on graph theory, it is not easy to study the various tools provided by complex network models. Therefore, in this paper, we attempt to introduce basic concepts of graph theory, including small-world networks and scale-free networks, and provide system models that can be easily implemented to be used as a powerful tool in solving various research problems related to IoT.

scholarly journals Modelling cascading failures in networks with the harmonic closeness

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0243801
Author(s):  
Yucheng Hao ◽  
Limin Jia ◽  
Yanhui Wang ◽  
Zhichao He
Keyword(s):  
Small World ◽  
Adjustable Parameter ◽  
Cascading Failures ◽  
Small World Networks ◽  
Scale Free ◽  
Low Load ◽  
Scale Free Networks ◽  
Initial Load ◽  
The Impact ◽  
Valuable Result

Many studies on cascading failures adopt the degree or the betweenness of a node to define its load. From a novel perspective, we propose an approach to obtain initial loads considering the harmonic closeness and the impact of neighboring nodes. Based on simulation results for different adjustable parameter θ, local parameter δ and proportion of attacked nodes f, it is found that in scale-free networks (SF networks), small-world networks (SW networks) and Erdos-Renyi networks (ER networks), there exists a negative correlation between optimal θ and δ. By the removal of the low load node, cascading failures are more likely to occur in some cases. In addition, we find a valuable result that our method yields better performance compared with other methods in SF networks with an arbitrary f, SW and ER networks with large f. Moreover, the method concerning the harmonic closeness makes these three model networks more robust for different average degrees. Finally, we perform the simulations on twenty real networks, whose results verify that our method is also effective to distribute the initial load in different real networks.

Research on Edge-Growing Models Related with Scale-Free Small-World Networks

2014 ◽  
Vol 513-517 ◽  
pp. 2444-2448 ◽  
Author(s):  
Bing Yao ◽  
Ming Yao ◽  
Xiang En Chen ◽  
Xia Liu ◽  
Wan Jia Zhang
Keyword(s):  
Complex Networks ◽  
Topological Structure ◽  
Spanning Trees ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Growing Network

Understanding the topological structure of scale-free networks or small world networks is required and useful for investigation of complex networks. We will build up a class of edge-growing network models and provide an algorithm for finding spanning trees of edge-growing network models in this article.

Information Networks as Complex Systems

2011 ◽  
pp. 43-58
Author(s):  
Yoshiteru Ishida
Keyword(s):  
Complex Systems ◽  
Complex Network ◽  
Normal State ◽  
Small World ◽  
Information Networks ◽  
Small World Networks ◽  
Scale Free ◽  
Abnormal State ◽  
Scale Free Networks ◽  
Spatial Prisoner’S Dilemma

Complex network such as scale-free networks and small-world networks have been studied with the dynamics when the information percolates through the networks. This chapter reports the problem of spreading the normal state (rather than spreading of the abnormal state) that is formalized as cleaning a contaminated network by mutual copying. Repairing by copying is the “double edged sword” that could spread contamination when properly used. A framework for controlling copying involving a spatial Prisoner’s Dilemma is introduced. Adaptive character to the network environment has been observed.

TOWARD A HARMONIOUS UNIFYING HYBRID MODEL FOR ANY EVOLVING COMPLEX NETWORKS

2007 ◽  
Vol 10 (02) ◽  
pp. 117-141 ◽  
Author(s):  
JINQING FANG ◽  
QIAO BI ◽  
YONG LI ◽  
XIN-BIAO LU ◽  
QIANG LIU
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Small World ◽  
Current Interest ◽  
Topological Properties ◽  
Small World Networks ◽  
Scale Free ◽  
Evolving Networks ◽  
Scale Free Networks ◽  
Hybrid Mechanisms

The current interest in complex networks is a part of a broader movement towards research on complex systems. Motivation of this work raises the two challenging questions: (i) Are real networks fundamentally random preferential attached without any deterministic attachment for both un-weighted and weighted networks? (ii) Is there a coherent physical idea and model for unifying the study of the formation mechanism of complex networks? To answer these questions, we propose a harmonious unifying hybrid preferential model (HUHPM) to a certain class of complex networks, which is controlled by a hybrid ratio, d/r, and study their behavior both numerically and analytically. As typical examples, we apply the concepts and method of the HUHPM to un-weighted scale-free networks proposed by Barabasi and Albert (BA), weighted evolving networks proposed by Barras, Bartholomew and Vespignani (BBV), and the traffic driven evolution (TDE) networks proposed by Wang et al., to get the so-called HUHPM-BA, HUHPM-BBV and HUHPM-TDE networks. All the findings of topological properties in the above three typical HUHPM networks give certain universal meaningful results which reveal some essential hybrid mechanisms for the formation of nontrivial scale-free and small-world networks.

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