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.

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.

Complex Systems in a Nutshell

2020 ◽  
pp. 19-32
Author(s):  
Megan S. Patterson ◽  
Michael K. Lemke ◽  
Jordan Nelon
Keyword(s):  
Complex Systems ◽  
Path Length ◽  
Path Dependence ◽  
Small World ◽  
Cardiometabolic Disease ◽  
Small World Networks ◽  
Stable States ◽  
Scale Free ◽  
Critical Transitions ◽  
Random Scale

This chapter provides an overview of the key foundational concepts and principles of the study of complex systems. First, a definition for system is provided, and the distinctions between complicated and complex systems are demarcated, as are detail, disorganized, organized, and dynamic types of complexity. Common properties across complex systems are defined and described, including stable states and steady states, path dependence, resilience, critical transitions and tipping points, early warning signals, feedback loops, and nonlinearity. This chapter also delves into how complex issues often consist of networks, with random, scale-free, and small world networks defined and network concepts such as degrees, path length, and heterogeneity defined. The concept of emergence is also emphasized, as well as related principles such as adaptation and self-organization. Cardiometabolic disease (and associated comorbidities) is used in this chapter as a thematic population health example.

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 An Extended Correlation Dimension of Complex Networks

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 710
Author(s):  
Sheng Zhang ◽  
Wenxiang Lan ◽  
Weikai Dai ◽  
Feng Wu ◽  
Caisen Chen
Keyword(s):  
Complex Networks ◽  
Correlation Dimension ◽  
Fractal Dimensions ◽  
Small World ◽  
Scaling Analysis ◽  
Fractal Nature ◽  
Small World Networks ◽  
Self Similarity ◽  
Weighted Networks ◽  
Fractal Properties

Fractal and self-similarity are important characteristics of complex networks. The correlation dimension is one of the measures implemented to characterize the fractal nature of unweighted structures, but it has not been extended to weighted networks. In this paper, the correlation dimension is extended to the weighted networks. The proposed method uses edge-weights accumulation to obtain scale distances. It can be used not only for weighted networks but also for unweighted networks. We selected six weighted networks, including two synthetic fractal networks and four real-world networks, to validate it. The results show that the proposed method was effective for the fractal scaling analysis of weighted complex networks. Meanwhile, this method was used to analyze the fractal properties of the Newman–Watts (NW) unweighted small-world networks. Compared with other fractal dimensions, the correlation dimension is more suitable for the quantitative analysis of small-world effects.

scholarly journals Afrikaans as a complex network: The word co-occurrence network in André P. Brink’s Donkermaan in Afrikaans, Dutch and English

2016 ◽  
Vol 35 (1) ◽  
Author(s):  
Burgert A. Senekal ◽  
Cornelia Geldenhuys
Keyword(s):  
Complex Systems ◽  
Network Model ◽  
Network Structure ◽  
Random Network ◽  
Small World ◽  
Distribution Patterns ◽  
Small World Networks ◽  
Scale Free ◽  
Free Network ◽  
Link Distribution

Language has already been approached as a system since De Saussure, and recently the theory of complex systems has been applied within Linguistics as well. Complex systems, however, can also be modelled as complex networks, and a variety of studies investigating the network structure of language have already been undertaken worldwide. The current study follows in the footsteps of overseas studies and investigates the network structure of Afrikaans by analysing a word co-occurrence network compiled from André P. Brink’s novel Donkermaan. Link distribution patterns and the small-world phenomenon are investigated and then compared to the English and Dutch translations of this novel. The current study represents the first network study of Afrikaans. Firstly, the random network model of Erdös and Rényi and the scale-free network model by Barabási and Albert are used to indicate that the link distribution patterns in a word co-occurrence network of Afrikaans are better described according to the network model of Barabási and Albert than by that of Erdös and Rényi. Furthermore, the method proposed by Humphreys and Gurney to define smallworldedness (S) was used to quantify this phenomenon for the Afrikaans, as well as English and Dutch versions of the text. With 522 ≤ S ≤ 797, it is indicated that Afrikaans, English and Dutch are all clearly small-world networks. Suggestions are also made for further research.

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.

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