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

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.

[1]  Giuseppe M. L. Sarnè,et al.  Forming time-stable homogeneous groups into Online Social Networks , 2017, Inf. Sci..

[2]  Marc Peter Deisenroth,et al.  Real-time community detection in full social networks on a laptop , 2018, PloS one.

[3]  Christos Faloutsos,et al.  Nonlinear Dynamics of Information Diffusion in Social Networks , 2017, ACM Trans. Web.

[4]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[5]  Laurent Massoulié,et al.  Self-organizing Flows in Social Networks , 2013, SIROCCO.

[6]  J. Reichardt,et al.  Statistical mechanics of community detection. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  David M. Raup,et al.  How Nature Works: The Science of Self-Organized Criticality , 1997 .

[8]  Three-parameter kinetics of a phase transition , 1996 .

[9]  M. Dubovikov,et al.  Dimension of the minimal cover and fractal analysis of time series , 2004 .

[10]  J. Forrest,et al.  The Evolution of Hyperedge Cardinalities and Bose-Einstein Condensation in Hypernetworks , 2015, Scientific reports.

[11]  Ming Li.  Fractal Time Series—A Tutorial Review , 2010 .

[12]  John Skvoretz,et al.  Complexity theory and models for social networks , 2002 .

[13]  M. Mitchell Waldrop,et al.  Complexity : the emerging science and the edge of order and chaos , 1992 .

[14]  Martin G. Everett,et al.  Role similarity and complexity in social networks , 1985 .

[15]  S. V. Maltseva,et al.  Model-Based Monitoring and Analysis of the Network Community Dynamics in a Textured State Space , 2014, 2014 IEEE 16th Conference on Business Informatics.

[16]  Muhammad Imran,et al.  Understanding Types of Users on Twitter , 2014, ArXiv.

[17]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[18]  João Gama,et al.  Social network analysis: An overview , 2018, WIREs Data Mining Knowl. Discov..

[19]  A. Grabowskia,et al.  Ising-based model of opinion formation in a complex network of interpersonal interactions , 2006 .

[20]  Victor Dmitriev,et al.  A Nonlinear Dynamical Approach to the Interpretation of Microblogging Network Complexity , 2017, COMPLEX NETWORKS.

[21]  Manuel Glez Bedia,et al.  Quantifying Political Self-Organization in Social Media. Fractal patterns in the Spanish 15M movement on Twitter , 2013, ECAL.

[22]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[23]  Self-organized criticality within fractional Lorenz scheme , 2003 .

[24]  R. D'Agostino,et al.  A Suggestion for Using Powerful and Informative Tests of Normality , 1990 .

[25]  Joachim Mathiesen,et al.  Emergent User Behavior on Twitter Modelled by a Stochastic Differential Equation , 2015, PloS one.

[26]  Roderick Melnik,et al.  Mechanisms of self-organized criticality in social processes of knowledge creation. , 2017, Physical review. E.

[27]  Przemyslaw Kazienko,et al.  Predicting community evolution in social networks , 2015, 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM).

[28]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[29]  Tijl De Bie,et al.  Detecting trends in twitter time series , 2016, 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP).

[30]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[31]  Tang,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[32]  Gonzalo Álvarez,et al.  A Model for Scale-Free Networks: Application to Twitter , 2015, Entropy.

[33]  Marija Mitrovic,et al.  Co-Evolutionary Mechanisms of Emotional Bursts in Online Social Dynamics and Networks , 2013, Entropy.

[34]  J. Bouchaud,et al.  Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights , 2015, PloS one.

[35]  A. Olemskoi.  REVIEWS OF TOPICAL PROBLEMS: Theory of stochastic systems with singular multiplicative noise , 1998 .

[36]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[37]  Stefan Bornholdt,et al.  Dynamics of social networks , 2003, Complex..

[38]  Sabre Kais,et al.  Degree distribution in quantum walks on complex networks , 2013, 1305.6078.

[39]  Mingzhou Ding,et al.  Estimating correlation dimension from a chaotic time series: when does plateau onset occur? , 1993 .

[40]  Pu Li,et al.  Ising Model of User Behavior Decision in Network Rumor Propagation , 2018 .

[41]  Bulakh Vitalii,et al.  Fractal time series analysis of social network activities , 2017, 2017 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T).

[42]  G. Bianconi.  Mean field solution of the Ising model on a Barabási–Albert network , 2002, cond-mat/0204455.

[43]  D J PRICE,et al.  NETWORKS OF SCIENTIFIC PAPERS. , 1965, Science.

[44]  Carter T. Butts,et al.  The complexity of social networks: theoretical and empirical findings , 2001, Soc. Networks.

[45]  H. Preissl,et al.  Detrended fluctuation analysis of short datasets : An application to fetal cardiac data , 2007 .

[46]  Raj Kumar Pan,et al.  Phase of Ising spins on modular networks analogous to social polarization. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.