Microscopic and Macroscopic Dynamics in Complex Networks

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Abstract:

The structure of complex networks has been a focal research topic over the past few decades. The discovery of structural patterns and regularities such as the ubiquitous power-law patterns evident in degree distributions, graph eigenvalues and human mobility patterns have provided the opportunity to model many different complex systems. However, the dynamics of networks remain a considerably less explored terrain. In our study we investigate the dynamics of networks both microscopically, by analyzing node-level evolution, and macroscopically, by investigating system-level dynamics. In particular, from the microscopic angle, we analyze the dynamics of relative popularity of individual nodes, as exhibited by their ranked degrees. We show that preferential principles do not apply to relative popularity evolution, and that it is rather governed by an inverse U-shaped curve, suggesting an inherent partition of the nodes into qualitatively distinct stability categories. From the macroscopic angle, we analyze the popularity dynamics from a system-level perspective, by examining the functional form of various distributions. Specifically, we address several intriguing questions — for how long are popular nodes expected to remain so? How much time is expected to pass between two consecutive popularity periods? What characterizes nodes which manage to maintain their popularity for long periods of time? Surprisingly, we find that such temporal aspects are governed by a power-law regime, and that these power-law regularities are equally likely across all node ages. We demonstrate our findings both empirically, by analyzing various large-scale real-world temporal datasets, and by developing theoretical models which reproduce these dynamical patterns and elucidate the enabling conditions for their formation. Our findings enhance the understanding of the dynamical processes systems undergo and provide plausible explanations to observed yet hitherto unexplained phenomena, such as how superstars fortify their ranks despite massive fluctuations in their degrees, and how stars are more prone to rank instability.

Bio:

Shahar Somin is a Ph.D student at the department of Industrial Engineering at Tel Aviv University, specializing in Network Science. Shahar holds a B.Sc. degree in Mathematics and Computer Science and an M.Sc. degree in Computer Science, both from the Hebrew University of Jerusalem. Her research is supervised by Prof. Erez Shmueli.

Contact:

• E-Mail: somin.shahar@gmail.com

• Linkedin: https://www.linkedin.com/in/shahar-somin-5522a98a