The Emergence of Scaling Law, Fractal Patterns and Small-World in Wireless Networks

Topology clustering, constructing overlay graphs, adding relay nodes, or creating a “small-world” network by building some shortcuts etc, topology control schemes are able to achieve the scalability, resilience, and fault-tolerance for wireless communication networks. In this article, we take a different approach to reach such aim for heterogeneous integrated wireless networks by generating a topology such that the resulting network is “scale-free”. Thereby we propose a topology control algorithm based on the “scale-free” complex network concept and directed proximity graph theory for integrated wireless networks with non-uniform transmission ranges. In this algorithm, the topology is also generated by new nodes’ growth and preferential attachment procedure, but where each new node connects to the existing nodes in its directed attachable proximity in terms of certain probability at each time step. Each node’s directed attachable proximity graph is generated from its directed reachable proximity graph that is built by regulating its transmission power based on locally collected information. The simulation experiments are provided to validate our claims.

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A meritocratic network formation model for the rise of social media influencers

Nature Communications ◽

10.1038/s41467-021-27089-8 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Nicolò Pagan ◽

Wenjun Mei ◽

Cheng Li ◽

Florian Dörfler

Keyword(s):

Online Social Networks ◽

Network Formation ◽

Preferential Attachment ◽

Scaling Law ◽

Small World ◽

Large Data ◽

Large Data Sets ◽

Directed Network ◽

Data Sets ◽

Quality Ranking

AbstractMany of today’s most used online social networks such as Instagram, YouTube, Twitter, or Twitch are based on User-Generated Content (UGC). Thanks to the integrated search engines, users of these platforms can discover and follow their peers based on the UGC and its quality. Here, we propose an untouched meritocratic approach for directed network formation, inspired by empirical evidence on Twitter data: actors continuously search for the best UGC provider. We theoretically and numerically analyze the network equilibria properties under different meeting probabilities: while featuring common real-world networks properties, e.g., scaling law or small-world effect, our model predicts that the expected in-degree follows a Zipf’s law with respect to the quality ranking. Notably, the results are robust against the effect of recommendation systems mimicked through preferential attachment based meeting approaches. Our theoretical results are empirically validated against large data sets collected from Twitch, a fast-growing platform for online gamers.

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A Small World Network Model for Energy Efficient Wireless Networks

IEEE Communications Letters ◽

10.1109/lcomm.2013.081313.131394 ◽

2013 ◽

Vol 17 (10) ◽

pp. 1928-1931 ◽

Cited By ~ 15

Author(s):

Tiankui Zhang ◽

Jinlong Cao ◽

Yue Chen ◽

Laurie Cuthbert ◽

Maged Elkashlan

Keyword(s):

Wireless Networks ◽

Network Model ◽

Energy Efficient ◽

Small World ◽

Small World Network

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An experimental study of small world network model for wireless networks

2015 36th IEEE Sarnoff Symposium ◽

10.1109/sarnof.2015.7324646 ◽

2015 ◽

Author(s):

Ziqian Dong ◽

Zheng Wang ◽

Wen Xie ◽

Obinna Emelumadu ◽

Chuanbi Lin ◽

...

Keyword(s):

Experimental Study ◽

Wireless Networks ◽

Network Model ◽

Small World ◽

Small World Network

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MICROSCOPIC SPIN MODEL FOR THE STOCK MARKET WITH ATTRACTOR BUBBLING ON REGULAR AND SMALL-WORLD LATTICES

International Journal of Modern Physics C ◽

10.1142/s0129183108012777 ◽

2008 ◽

Vol 19 (07) ◽

pp. 1035-1045 ◽

Cited By ~ 3

Author(s):

A. KRAWIECKI

Keyword(s):

Time Series ◽

Stock Market ◽

Scaling Law ◽

Small World ◽

Spin Model ◽

Volatility Clustering ◽

Wide Range ◽

Regular Lattices ◽

Multi Agent ◽

Yield Time

A multi-agent spin model for changes of prices in the stock market based on the Ising-like cellular automaton with interactions between traders randomly varying in time is investigated by means of Monte Carlo simulations. The structure of interactions has topology of a small-world network obtained from regular two-dimensional square lattices with various coordination numbers by randomly cutting and rewiring edges. Simulations of the model on regular lattices do not yield time series of logarithmic price returns with statistical properties comparable with the empirical ones. In contrast, in the case of networks with a certain degree of randomness for a wide range of parameters the time series of the logarithmic price returns exhibit intermittent bursting typical of volatility clustering. Also the tails of distributions of returns obey a power scaling law with exponents comparable to those obtained from the empirical data.

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