Time-Varying Hyperbolic Geometric Graphs–TV-HGGs

Project summary: Previously we discovered a powerful and unique geometric framework explaining the ubiquitous common structure of complex networks and linking this structure to the optimality of their common functions. In this framework, network nodes are mapped to points in hyperbolic spaces, which lie beneath the observable topologies. The analysis of complex networks is then simplified significantly, as their discrete complex structure can be studied in purely geometric terms. This framework, known as hyperbolic geometric graphs (HGGs), has attracted a great deal of interest in mathematics, physics, computer science and biology. However, despite several years of research, our knowledge and understanding of network geometry is essentially still limited to static HGGs and methods that can only infer the geometry of network snapshots. But real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links, and there currently exists no principled theory that can model and predict their dynamics — a grand-challenge open problem in modern network theory. The main aim of this project is to address this challenge by mapping the general problem of predicting network dynamics to the specific problem of predicting the motion of nodes in their hidden hyperbolic spaces and developing models of time-varying hyperbolic geometric graphs.

To this end, we aim to:
(i) analyze and capture the motion of nodes in the hyperbolic spaces of real networks using stochastic differential equations;

(ii) develop sound generative models of time-varying hyperbolic geometric graphs (TV-HGGs), which can explain the dynamical properties of real-world networks; and

(iii) develop statistical inference methods able to forecast future connections and disconnections in dynamic networks over different time scales.

Duration: 2/10/2020-31/3/2023.
Funded by: Cyprus Research & Innovation Foundation.
Budget: €560400.

The team

Prof. F. Papadopoulos

Fragkiskos Papadopoulos is an Associate Professor of the Department of Electrical Engineering, Computer Engineering and Informatics at Cyprus University of Technology. He was previously an Assistant Professor (2015-2020) and a Lecturer (2011-2015) at the same department. He received the Diploma in Electrical and Computer Engineering from the National Technical University of Athens in 2002. In 2004 and 2007 he received respectively the MSc and PhD degrees in Electrical Engineering from the University of Southern California, Los Angeles. During 2007-2009 he was a postdoctoral researcher at the Center for Applied Internet Data Analysis (CAIDA) at the University of California, San Diego. He was also a visiting Lecturer at the department of Electrical and Computer Engineering of the University of Cyprus (2009-2010). His research focuses on the theory and foundations of complex networks and their real-world applications. Topics of interest include: network geometry, network navigation, statistical inference and hyperbolic network embedding, dynamics prediction, multiplex networks, temporal networks, and performance analysis of communication networks. His research has been published in major peer reviewed international scientific journals, including Nature, Nature Physics, Nature Communications, and Physical Review Letters. He is a co-director of the NetSySci Research Laboratory.

Dr. M. A. Rodriguez-Flores
(Postdoctoral Researcher)

Dr. Marco Antonio Rodriguez Flores was a postdoctoral Researcher at NetSySci Research Laboratory, Cyprus University of Technology. He has completed his doctoral degree in December of 2020 under the direction of Prof. Fragkiskos Papadopoulos at Cyprus University of Technology. His research interests lie in the field of complex networks, including: human proximity networks, network geometry and network dynamics.

(Jan. 2021 – Apr. 2022)

Dr. S. Zambirinis
(Postdoctoral Researcher)

Dr. Sofoclis Zambirinis is a postdoctoral Researcher at NetSySci Research Laboratory, Cyprus University of Technology. He has a BSc in Mathematics (University of Athens, GPA 9.4/10, academically ranked in the top 1% of his graduating class), an MPhil in Statistical Science (University of Cambridge), and a PhD in Management Science (Lancaster University), with specialization in optimization in vehicle routing and scheduling. During his doctoral studies, his research interests included the following: mathematical programming, combinatorial optimization, multi-objective optimization, metaheuristic algorithms, vehicle routing and scheduling problems, transportation systems, and disruption management. His current research lies in the field of complex networks, focusing on time-varying hyperbolic geometric graphs, temporal networks, and network geometry.

(Feb. 2021 – Present)

Dr. C. Iordanou
(Postdoctoral Researcher)

Costas Iordanou is currently a postdoctoral researcher at the Network Systems and Science Research Laboratory (NetSySci), Cyprus University of Technology. Prior to that he was holding a postdoctoral position at the Max Planck Institute for Informatics, Germany. During his PhD studies he was fully funded by an FP7 EU grant (Marie Curie, Metrics ITN program), a collaboration between Universidad Carlos III de Madrid, Technical University of Berlin and Telefonica I + D. His research interest focuses on measuring the extent of targeted advertising taking place on the wired and wireless web, establishing causality between observed targeted advertisements and past browsing behavior, and developing tools and obfuscation techniques for preserving one’s privacy in view of the revealed targeted advertisement methods. He received a BSc. in Computer Engineering and Informatics (2013) from Cyprus University of Technology and MSc in Computer Engineering and Informatics (2014) from the same university. In 2015 he also received a second MSc. in Telematic Engineering from Universidad Carlos III de Madrid. In 2019 he receive his PhD (-Dr. -Ing.) from the Technische Universität Berlin. As part of his PhD studies, he worked on the design and implementation of multiple crowdsourced web-based distributed systems that aim to help internet users to understand how their personal data are collected and used on the internet.

(Mar. 2021 – Present)

Evangelos Papaefthymiou, is a Post-doctoral Researcher at NetSySci Research Laboratory, Cyprus University of Technology. Evangelos Papaefthymiou holds a PhD in Applied Mathematics from the Department of Mathematics of Imperial College London (2014). His PhD work led to publications in top journals in the field of Applied Mathematics and he was awarded the Yael Naim Dowker Centenary Prize in Mathematics for the best thesis in the Department of Mathematics. Furthermore, he holds a Meng degree (5-years of studies, 2002-2007) from the Department of Mechanical and Aeronautical Engineering Department of the University of Patras.

(Jun. 2022 – Present)


  1. Embedding-aided network dismantling, Saeed Osat, Fragkiskos Papadopoulos, Andreia Sofia Teixeira, and Filippo Radicchi, Physical Review Research, Vol. 5, Issue 1, February 2023.
  2. Dynamics of cold random hyperbolic graphs with link persistence, Sofoclis Zambirinis, Harrison Hartle, and Fragkiskos Papadopoulos, Physical Review E, Vol. 106, Issue 6, December 2022. (arXiv)
  3. Population-wide measures due to the COVID-19 pandemic and exposome changes in the general population of Cyprus in March-May 2020, Xanthi Andrianou, Corina Konstantinou, Marco A. Rodríguez-Flores, Fragkiskos Papadopoulos, and Konstantinos Makris, BMC Public Health, Vol. 22, No. 2279, December 2022.
  4. Topology and Geometry of the Third-Party Domains Ecosystem: Measurement and Applications, Costas Iordanou and Fragkiskos Papadopoulos, ACM SIGCOMM Computer Communication Review (CCR), Vol. 52, Issue 4, October 2022. (arXiv)
  5. Dynamics of hot random hyperbolic graphs, Fragkiskos Papadopoulos and Sofoclis Zambirinis, Physical Review E, Vol. 105, Issue 2, February 2022. (arXiv)
  6. Dynamic Hidden-Variable Network Models, Harrison Hartle, Fragkiskos Papadopoulos, and Dmitri Krioukov, Physical Review E, Vol. 103, Issue 5, May 2021. (arXiv)
  7. Hyperbolic Mapping of Human Proximity Networks, Marco A. Rodríguez-Flores and Fragkiskos Papadopoulos, Scientific Reports, Vol. 10, No. 20244, November 2020.
  8. Weighted hypersoft configuration model, Ivan Voitalov, Pim van der Hoorn, Maksim Kitsak, Fragkiskos Papadopoulos, and Dmitri Krioukov, Physical Review Research, Vol. 2, Issue 4, October 2020. (code)