Scale-free Effects Research Articles

Small-world and scale-free effects of complex networks generated by a self-similar fractal

In this paper, we construct a class of growing networks by the encoding method of the iterated function system based on a planar self-similar fractal, and demonstrate that the networks have small-world and scale-free effects.

FRACTAL NETWORKS MODELED BY SOME FRACTAL CARPET

We construct a family of evolving networks modeled by some fractal carpet which is not symmetric. We investigate the scale-free effect and small-word effect of our fractal networks, including the power-law of the cumulative degree distribution, the average clustering coefficient and the average geodesic distance.

Fractal networks on 4m-sided Dürer-type polygon

Dürer’s pentagon is known to the artist Albrecht Dürer, whose work has produced an effect on modern telecommunication. In this paper, we consider directed networks generated by Dürer-type polygons, which is based on an [Formula: see text]-sided polygon where [Formula: see text] and [Formula: see text]. This object is quite different from what we previously studied when [Formula: see text] is not a multiple of 4. We aim to study some properties of these networks, such as degree distribution, clustering coefficient and average path length. We show that such networks have the scale-free effect, but do not have the small-world effect. It is expected that our results will provide certain theoretical support to further applications in modern telecommunication.

FRACTAL NETWORKS ON DÜRER-TYPE POLYGON

Dürer’s pentagon is known to the artist Albrecht Dürer. In this paper, we consider directed networks generated by Dürer-type polygons. We aim to present a study on some properties of these networks, such as degree distribution, clustering coefficient and average path length. We show that such networks have the scale-free effect, but do not have the small-world effect.

Comprehensive Study of Evolution of Global Environmental Quality Research Using Informetric Co-Word Network

Global environmental quality is a rapidly developing and complicated subject in need of a new method for evolutionary analyses. This paper proposes an informetric dynamic co-word network to study the evolution of global environmental quality research (GEQR), making a significant contribution to the available literature. First, it was observed that GEQR has been vigorously developing and hotspots have emerged through a self-organized adjustment process, which other methods lacked. Second, small-world and scale-free effects, which are mechanisms of an evolving knowledge system (KS), were identified in GEQR’s KS. Third, the dynamic co-word network yielded topological patterns and robust clustering in GEQR. An assessment strategy map/table of GEQR has been accordingly proposed as a mined innovative function of co-word networks, which provides new holistic understanding of global environmental quality. Thus, our studies on GEQR evolution using this informetric dynamic co-word network method may help researchers or managers learn GEQR development mechanisms, allowing for further topical selection and policy management of GEQR. Beyond GEQR, the informetric dynamic co-word network method may also provide a new universal method for evolutionary analysis of many other environmental problems.

Seven decades of chemotherapy clinical trials: a pan-cancer social network analysis

Clinical trials establish the standard of cancer care, yet the evolution and characteristics of the social dynamics between the people conducting this work remain understudied. We performed a social network analysis of authors publishing chemotherapy-based prospective trials from 1946 to 2018 to understand how social influences, including the role of gender, have influenced the growth and development of this network, which has expanded exponentially from fewer than 50 authors in 1946 to 29,197 in 2018. While 99.4% of authors were directly or indirectly connected by 2018, our results indicate a tendency to predominantly connect with others in the same or similar fields, as well as an increasing disparity in author impact and number of connections. Scale-free effects were evident, with small numbers of individuals having disproportionate impact. Women were under-represented and likelier to have lower impact, shorter productive periods (P < 0.001 for both comparisons), less centrality, and a greater proportion of co-authors in their same subspecialty. The past 30 years were characterized by a trend towards increased authorship by women, with new author parity anticipated in 2032. The network of cancer clinical trialists is best characterized as strategic or mixed-motive, with cooperative and competitive elements influencing its appearance. Network effects such as low centrality, which may limit access to high-profile individuals, likely contribute to the observed disparities.

How do urban mobility (geo)graph\u2019s topological properties fill a map?

Urban mobility data are important to areas ranging from traffic engineering to the analysis of outbreaks and disasters. In this paper, we study mobility data from a major Brazilian city from a geographical viewpoint using a Complex Network approach. The case study is based on intra-urban mobility data from the Metropolitan area of Rio de Janeiro (Brazil), presenting more than 480 spatial network nodes. While for the mobility flow data a log-normal distribution outperformed the power law, we also found moderate evidence for scale-free and small word effects in the flow network’s degree distribution. We employ a novel open-source GIS tool to display (geo)graph’s topological properties in maps and observe a strong traffic-topology association and also a fine adjustment for hubs location for different flow threshold networks. In the central commercial area for lower thresholds and in high population residential areas for higher thresholds. This set of results, including statistical, topological and geographical analysis may represent an important tool for policymakers and stakeholders in the urban planning area, especially by the identification of zones with few but strong links in a real data-driven mobility network.

FRACTALITY OF SUBSTITUTION NETWORKS

Using the covering theory in fractal geometry, we obtain the fractality of self-similar substitution networks introduced by Li et al. [Scale-free effect of substitution networks, Physica A 492 (2018) 1449–1455].

Structural features and evolutionary mechanisms of industrial symbiosis networks: Comparable analyses of two different cases

Recently, industrial symbiosis networks (ISNs) have become popular development patterns for regional industrial systems in many countries. As such, it is important to analyze the underlying structural characteristics and evolutionary mechanisms of ISNs in diverse situations. This paper's contributions to the literature are threefold. (1) Based on all types of centrality and centralization measures in social networks (the direction of links included), the structural similarities, differences, and associated mechanisms of two typical and comparable ISNs—the spontaneously formed Kalundborg ISN in Denmark and the planned Lubei ISN in China are the first to be revealed. (2) Based on average clustering coefficient, average path length, and power law distribution of degree from complex network theory, the small-world and scale-free effects of the two ISNs are compared. (3) Network fragmentation is then defined to compare the two ISNs under the selective attack of removing critical enterprises from them at different development stages. As such, this paper not only extends the methodology of analyzing the structural characteristics of different ISNs, but also provides guidance for managers on the construction of actual eco-industrial parks.

Scale-free effect of substitution networks

In this paper, we construct the growing networks in terms of substitution rule. Roughly speaking, we replace edges of different colors with different initial graphs. Then the evolving networks are constructed. We obtained the free-scale effect of our substitution networks.

A dynamic co-word network-related approach on the evolution of China’s urbanization research

In recent years, China's urbanization has developed very quickly. Many scholars have conducted China's urbanization research (CUR) and have published a large number of articles. With CUR as a case, we construct the dynamic co-word network to analyze the characteristics of development about the knowledge system (KS). We draw several conclusions from this research. (1) The development of CUR possesses small-world characteristics and scale-free effects. The co-word network of CUR increases significantly to a large-scale network. (2) Betweenness centrality and eigenvector centrality of the dynamic co-word networks positively correlate with node degree. The popular nodes connecting with a large number of topics are also the nodes that occur in the critical paths. The popular keywords in CUR also bridge distant clusters of the related topics. (3) The clustering coefficients indicate that a number of topics with low degrees tend to relate to the adjacent topics more directly to form "conglobation" clusters. The network is a hierarchical clustered structure. The hub keywords play a crucial role in bridging distinct clusters of highly associated keywords and make them form an integrated network. (4) Since 2003, the CUR has begun to develop systematically. From 1998 to 2015, the hotspots in CUR varied diversely, which are highly correlated with social issues and public concerns. (5) We proposed several practical implications on the development of CUR from the dynamic co-word network measures. Beyond the case of CUR's KS, we hope the versatility of methods in this research also provides enlightenment for other KS studies.

Fractality and scale-free effect of a class of self-similar networks

In this paper, given an initial directed graph as a self-similar pattern and fix two nodes in the pattern, we can iterate the graph by replacing any directed edge with the initial graph of pattern and identifying the fixed nodes of pattern with the endpoints of directed edge. Using the iteration again and again, we obtain a family of growing self-similar networks. Modify these networks to be undirected ones, we obtain growing self-similar undirected networks. We obtain the fractality of our self-similar networks and find out the scale-free effect in terms of the matrix related to two fixed nodes in the initial graph.

Assessing Equality of Means Using the Overlap of Range-Preserving Confidence Intervals

ABSTRACTHypothesis testing procedures where equality of means is assessed at a prespecified level based on the (non-)overlap of confidence intervals are discussed. Assessing statistical significance via the (non-)overlap of two confidence intervals with an appropriate confidence level provides a simple and effective way of visually understanding statistical results. This article extends previous approaches by considering range-preserving confidence intervals where the values in such intervals are in the allowable range of the parameter of interest. To obtain reliable procedures, appropriate effective degrees of freedom are suggested by considering the Welch-Satterthwaite equation for both independent two-sample and paired-sample cases. The proposed procedures also allow users to express results in terms of commonly used scale-free effect sizes, which are highly useful for interpreting parameters of interest. Simulation results suggest that the proposed procedures may be robust to unequal or small sample sizes, nonnormal distributions, heterogeneous variances, and various degrees of correlation. A real-life application from a study in cognitive psychology illustrates the effectiveness of the proposed procedures.

A SMALL-WORLD AND SCALE-FREE NETWORK GENERATED BY SIERPINSKI TETRAHEDRON

The Sierpinski tetrahedron is used to construct evolving networks, whose vertexes are all solid regular tetrahedra in the construction of the Sierpinski tetrahedron up to the stage [Formula: see text] and any two vertexes are neighbors if and only if the corresponding tetrahedra are in contact with each other on boundary. We show that such networks have the small-world and scale-free effects, but are not fractal scaling.

A small-world and scale-free network generated by Sierpinski Pentagon

The Sierpinski Pentagon is used to construct evolving networks, whose nodes are all solid regular pentagons in the construction of the Sierpinski Pentagon up to the stage t and any two nodes are neighbors if and only if the intersection of corresponding pentagons is non-empty and non-singleton. We show that such networks have the small-world and scale-free effects, but are not fractal scaling.

Complex Networks: Statistical Properties, Community Structure, and Evolution

We investigate the function for different networks based on complex network theory. In this paper, we choose five data sets from various areas to study. In the study of Chinese network, scale-free effect and hierarchical structure features are found in this complex system. These results indicate that the discovered features of Chinese character structure reflect the combination nature of Chinese characters. In addition, we study the community structure in Chinese character network. We can find that community structure is always considered as one of the most significant features in complex networks, and it plays an important role in the topology and function of the networks. Furthermore, we cut all the nodes in the different networks from low degree to high degree and then obtain many networks with different scale. According to the study, two interesting results have been obtained. First, the relationship between the node number of the maximum communities and the number of communities in the corresponding networks is studied and it is linear. Second, when the number of nodes in the maximum communities is increasing, the increasing tendency of the number of its edges slows down; we predict the complex networks have sparsity. The study effectively explains the characteristic and community structure evolution on different networks.

Robust and scale-free effect sizes for non-Normal two-sample comparisons, with applications in e-commerce

The effect size (ES) has been mainly introduced and investigated for changes in location under an assumption of Normality for the underlying population. However, there are many circumstances where populations are non-Normal, or depend on scale and shape and not just a location parameter. Our motivating application from e-commerce requires an ES which is appropriate for long-tailed distributions. We review some common ES measures. We then introduce two novel alternative ES for two-sample comparisons, one scale-free and one on the original scale of measurement, and analyse some theoretical properties. We examine these ES for two-sample comparison studies under an assumption of Normality and investigate what happens when both location and scale parameters differ. We explore ES for phenomena for non-Normal situations, using the Weibull family for illustration. Finally, for an application, we assess differences in customer behaviour when browsing E-commerce websites.

Deterministic scale-free small-world networks of arbitrary order

In many real-life networks, both the scale-free distribution of degree and small-world behavior are important features. There are many random or deterministic models of networks to simulate these features separately. However, there are few models that combine the scale-free effect and small-world behavior, especially in terms of deterministic versions. What is more, all the existing deterministic algorithms running in the iterative mode generate networks with only several discrete numbers of nodes. This contradicts the purpose of creating a deterministic network model on which we can simulate some dynamical processes as widely as possible. According to these facts, this paper proposes a deterministic network generation algorithm, which can not only generate deterministic networks following a scale-free distribution of degree and small-world behavior, but also produce networks with arbitrary number of nodes. Our scheme is based on a complete binary tree, and each newly generated leaf node is further linked to its full brother and one of its direct ancestors. Analytical computation and simulation results show that the average degree of such a proposed network is less than 5, the average clustering coefficient is high (larger than 0.5, even for a network of size 2 million) and the average shortest path length increases much more slowly than logarithmic growth for the majority of small-world network models.

Local-Global Interaction and the Emergence of Scale-Free Networks with Community Structures

Understanding complex networks in the real world is a nontrivial task. In the study of community structures we normally encounter several examples of these networks, which makes any statistical inferencing a challenging endeavor. Researchers resort to computer-generated networks that resemble networks encountered in the real world as a means to generate many networks with different sizes, while maintaining the real-world characteristics of interest. The generation of networks that resemble the real world turns out in itself to be a complex search problem. We present a new rewiring algorithm for the generation of networks with unique characteristics that combine the scale-free effects and community structures encountered in the real world. The algorithm is inspired by social interactions in the real world, whereby people tend to connect locally while occasionally they connect globally. This local-global coupling turns out to be a powerful characteristics that is required for our proposed rewiring algorithm to generate networks with community structures, power law distributions both in degree and in community size, positive assortative mixing by degree, and the rich-club phenomenon.

Scale free effects in world currency exchange network

A large collection of daily time series for 60 world currencies' exchange rates is considered. The correlation matrices are calculated and the corresponding Minimal Spanning Tree (MST) graphs are constructed for each of those currencies used as reference for the remaining ones. It is shown that multiplicity of the MST graphs' nodes to a good approximation develops a power like, scale free distribution with the scaling exponent similar as for several other complex systems studied so far. Furthermore, quantitative arguments in favor of the hierarchical organization of the world currency exchange network are provided by relating the structure of the above MST graphs and their scaling exponents to those that are derived from an exactly solvable hierarchical network model. A special status of the USD during the period considered can be attributed to some departures of the MST features, when this currency (or some other tied to it) is used as reference, from characteristics typical to such a hierarchical clustering of nodes towards those that correspond to the random graphs. Even though in general the basic structure of the MST is robust with respect to changing the reference currency some trace of a systematic transition from somewhat dispersed – like the USD case – towards more compact MST topology can be observed when correlations increase.