Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science

Andrey Dmitriev,Svetlana Maltseva,Vasily Kornilov

doi:10.1155/2018/4732491

Andrey Dmitriev, Svetlana Maltseva + Show 1 more

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https://doi.org/10.1155/2018/4732491

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Abstract

Recent developments in nonlinear science have caused the formation of a new paradigm called the paradigm of complexity. The self-organized criticality theory constitutes the foundation of this paradigm. To estimate the complexity of a microblogging social network, we used one of the conceptual schemes of the paradigm, namely, the system of key signs of complexity of the external manifestations of the system irrespective of its internal structure. Our research revealed all the key signs of complexity of the time series of a number of microposts. We offer a new model of a microblogging social network as a nonlinear random dynamical system with additive noise in three-dimensional phase space. Implementations of this model in the adiabatic approximation possess all the key signs of complexity, making the model a reasonable evolutionary model for a microblogging social network. The use of adiabatic approximation allows us to model a microblogging social network as a nonlinear random dynamical system with multiplicative noise with the power-law in one-dimensional phase space.

Highlights

Social networks have been studied longer than any other type of networks
The empirical time series of microposts has all the key properties of complexity: a power-law probability density function (PDF), noise that is close to flicker noise, time correlations with long memory, and scale invariance in a time series of microposts
The time series of microposts is characterized by scale invariance; i.e., it is a fractal time series

Summary

Introduction

Social networks have been studied longer than any other type of networks. It is remarkable that one of the signs of network complexity—a power law of nodes’ degree distribution [1]—was first empirically formulated by D. A small number of nodes have a large number of connections, whereas a large number of nodes have just a few connections This name was not invented for this type of networks. It came from the theory of critical phenomena, where fluctuations in critical states follow a power law. The theory of scale-free networks is considered to be one of the scenarios complex systems follow when they come into a critical state. As of late, such networks are more often called complex networks

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