Sublinear domination and core–periphery networks

AbstractAn important question in representative democracies is how to determine the optimal parliament size of a given country. According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with an exponent equal to 1/3, between the size of an elected parliament and the country’s population. Empirical data in modern European countries support such universality but are consistent with a larger exponent. In this work, we analyse this intriguing regularity using tools from complex networks theory. We model the population of a democratic country as a random network, drawn from a growth model, where each node is assigned a constituency membership sampled from an available set of size D. We calculate analytically the modularity of the population and find that its functional relation with the number of constituencies is strongly non-monotonic, exhibiting a maximum that depends on the population size. The criterion of maximal modularity allows us to predict that the number of representatives should scale as a power-law in the size of the population, a finding that is qualitatively confirmed by the empirical analysis of real-world data.

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Analysis on Invulnerability of Wireless Sensor Network towards Cascading Failures Based on Coupled Map Lattice

Complexity ◽

10.1155/2018/6386324 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14 ◽

Cited By ~ 4

Author(s):

Xiuwen Fu ◽

Yongsheng Yang ◽

Haiqing Yao

Keyword(s):

Random Network ◽

Small World ◽

Coupled Map Lattice ◽

Wireless Sensor ◽

Cascading Failures ◽

Scale Free Network ◽

Scale Free ◽

Network Topologies ◽

Free Network ◽

Entire Network

Previous research of wireless sensor networks (WSNs) invulnerability mainly focuses on the static topology, while ignoring the cascading process of the network caused by the dynamic changes of load. Therefore, given the realistic features of WSNs, in this paper we research the invulnerability of WSNs with respect to cascading failures based on the coupled map lattice (CML). The invulnerability and the cascading process of four types of network topologies (i.e., random network, small-world network, homogenous scale-free network, and heterogeneous scale-free network) under various attack schemes (i.e., random attack, max-degree attack, and max-status attack) are investigated, respectively. The simulation results demonstrate that the rise of interference R and coupling coefficient ε will increase the risks of cascading failures. Cascading threshold values Rc and εc exist, where cascading failures will spread to the entire network when R>Rc or ε>εc. When facing a random attack or max-status attack, the network with higher heterogeneity tends to have a stronger invulnerability towards cascading failures. Conversely, when facing a max-degree attack, the network with higher uniformity tends to have a better performance. Besides that, we have also proved that the spreading speed of cascading failures is inversely proportional to the average path length of the network and the increase of average degree k can improve the network invulnerability.

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Factor or Network Model? Predictions From Neural Networks

Journal of Behavioral Data Science ◽

10.35566/jbds/v1n1/p5 ◽

2021 ◽

Vol 1 (1) ◽

Author(s):

Alexander P. Christensen ◽

Keyword(s):

Neural Networks ◽

Network Model ◽

Latent Variable ◽

Random Network ◽

Network Models ◽

Small World ◽

Small World Network ◽

Monte Carlo Simulation Study ◽

Psychological Phenomena ◽

The Neural Networks

The nature of associations between variables is important for constructing theory about psychological phenomena. In the last decade, this topic has received renewed interest with the introduction of psychometric network models. In psychology, network models are often contrasted with latent variable (e.g., factor) models. Recent research has shown that differences between the two tend to be more substantive than statistical. One recently developed algorithm called the Loadings Comparison Test (LCT) was developed to predict whether data were generated from a factor or small-world network model. A significant limitation of the current LCT implementation is that it's based on heuristics that were derived from descriptive statistics. In the present study, we used artificial neural networks to replace these heuristics and develop a more robust and generalizable algorithm. We performed a Monte Carlo simulation study that compared neural networks to the original LCT algorithm as well as logistic regression models that were trained on the same data. We found that the neural networks performed as well as or better than both methods for predicting whether data were generated from a factor, small-world network, or random network model. Although the neural networks were trained on small-world networks, we show that they can reliably predict the data-generating model of random networks, demonstrating generalizability beyond the trained data. We echo the call for more formal theories about the relations between variables and discuss the role of the LCT in this process.

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Specialization Models of Network Growth

Journal of Complex Networks ◽

10.1093/comnet/cny024 ◽

2018 ◽

Vol 7 (3) ◽

pp. 375-392 ◽

Cited By ~ 1

Author(s):

L A Bunimovich ◽

D C Smith ◽

B Z Webb

Keyword(s):

Power Law ◽

Network Topology ◽

Real World ◽

Degree Distribution ◽

Small World ◽

Hierarchical Network ◽

Network Growth ◽

Complex Tasks ◽

Small World Property ◽

Law Degree

AbstractOne of the most important features observed in real networks is that, as a network’s topology evolves so does the network’s ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain subnetworks begin to specialize the function(s) they perform. Herein, we introduce a class of models of network growth based on this notion of specialization and show that as a network is specialized using this method its topology becomes increasingly sparse, modular and hierarchical, each of which are important properties observed in real networks. This procedure is also highly flexible in that a network can be specialized over any subset of its elements. This flexibility allows those studying specific networks the ability to search for mechanisms that describe their growth. For example, we find that by randomly selecting these elements a network’s topology acquires some of the most well-known properties of real networks including the small-world property, disassortativity and a right-skewed degree distribution. Beyond this, we show how this model can be used to generate networks with real-world like clustering coefficients and power-law degree distributions, respectively. As far as the authors know, this is the first such class of models that can create an increasingly modular and hierarchical network topology with these properties.

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Local rewiring algorithms to increase clustering and grow a small world

Journal of Complex Networks ◽

10.1093/comnet/cny032 ◽

2018 ◽

Vol 7 (4) ◽

pp. 564-584

Author(s):

Jeff Alstott ◽

Christine Klymko ◽

Pamela B Pyzza ◽

Mary Radcliffe

Keyword(s):

Community Structure ◽

Real World ◽

Path Length ◽

Random Network ◽

Small World ◽

Single Edge ◽

Network Properties ◽

Clustered Network

Abstract Many real-world networks have high clustering among vertices: vertices that share neighbours are often also directly connected to each other. A network’s clustering can be a useful indicator of its connectedness and community structure. Algorithms for generating networks with high clustering have been developed, but typically rely on adding or removing edges and nodes, sometimes from a completely empty network. Here, we introduce algorithms that create a highly clustered network by starting with an existing network and rearranging edges, without adding or removing them; these algorithms can preserve other network properties even as the clustering increases. They rely on local rewiring rules, in which a single edge changes one of its vertices in a way that is guaranteed to increase clustering. This greedy step can be applied iteratively to transform a random network into a form with much higher clustering. Additionally, the algorithms presented grow a network’s clustering faster than they increase its path length, meaning that network enters a regime of comparatively high clustering and low path length: a small world. These algorithms may be a basis for how real-world networks rearrange themselves organically to achieve or maintain high clustering and small-world structure.

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Preprocessing Rules for Target Set Selection in Complex Networks

10.5753/brasnam.2020.11167 ◽

2020 ◽

Author(s):

Renato Silva Melo ◽

André Luís Vignatti

Keyword(s):

Complex Networks ◽

Power Law ◽

Real World ◽

Degree Distribution ◽

Topological Properties ◽

Input Graph ◽

Target Set ◽

Law Degree ◽

Entire Network ◽

Target Set Selection

In the Target Set Selection (TSS) problem, we want to find the minimum set of individuals in a network to spread information across the entire network. This problem is NP-hard, so find good strategies to deal with it, even for a particular case, is something of interest. We introduce preprocessing rules that allow reducing the size of the input without losing the optimality of the solution when the input graph is a complex network. Such type of network has a set of topological properties that commonly occurs in graphs that model real systems. We present computational experiments with real-world complex networks and synthetic power law graphs. Our strategies do particularly well on graphs with power law degree distribution, such as several real-world complex networks. Such rules provide a notable reduction in the size of the problem and, consequently, gains in scalability.

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

Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie ◽

10.4102/satnt.v35i1.1368 ◽

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.

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Dimensionality of Social Networks Using Motifs and Eigenvalues

10.32920/14668887.v1 ◽

2021 ◽

Author(s):

Anthony Bonato ◽

David F. Gleich ◽

Myunghwan Kim ◽

Dieter Mitsche ◽

Paweł Prałat ◽

...

Keyword(s):

Social Networks ◽

Social Network ◽

Network Model ◽

Power Law ◽

Metric Space ◽

Real World ◽

Eigenvalue Distribution

We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an m-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when m scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the distribution of motif counts, and the second exploits the eigenvalue distribution.

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Distribution of Node Characteristics in Evolving Tripartite Network

Entropy ◽

10.3390/e22030263 ◽

2020 ◽

Vol 22 (3) ◽

pp. 263 ◽

Cited By ~ 2

Author(s):

Ladislav Beranek ◽

Radim Remes

Keyword(s):

Network Model ◽

Power Law ◽

Real World ◽

Strength Distribution ◽

Growth Mechanisms ◽

Preferential Growth ◽

Basic Properties ◽

And Behavior

Many real-world networks have a natural tripartite structure. Investigating the structure and the behavior of actors in these networks is useful to gain a deeper understanding of their behavior and dynamics. In our paper, we describe an evolving tripartite network using a network model with preferential growth mechanisms and different rules for changing the strength of nodes and the weights of edges. We analyze the characteristics of the strength distribution and behavior of selected nodes and selected actors in this tripartite network. The distributions of these analyzed characteristics follow the power-law under different modeled conditions. Performed simulations have confirmed all these results. Despite its simplicity, the model expresses well the basic properties of the modeled network. It can provide further insights into the behavior of systems with more complex behaviors, such as the multi-actor e-commerce system that we have used as a real basis for the validation of our model.

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Dimensionality of Social Networks Using Motifs and Eigenvalues

10.32920/14668887 ◽

2021 ◽

Author(s):

Anthony Bonato ◽

David F. Gleich ◽

Myunghwan Kim ◽

Dieter Mitsche ◽

Paweł Prałat ◽

...

Keyword(s):

Social Networks ◽

Social Network ◽

Network Model ◽

Power Law ◽

Metric Space ◽

Real World ◽

Eigenvalue Distribution

We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an m-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when m scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the distribution of motif counts, and the second exploits the eigenvalue distribution.

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