What is a complex system? What is network science?

A Complex system is broadly defined as a system in which the interactions of many elements lead to the emergence of unexpected collective behaviors. Examples can be found in every corner of our lives at every scale: human societies, cells, brains, organisms, ecosystems, evolution, epidemics, languages, culture and norms, mobility and migration, information and communication systems, cities and transportation systems, infrastructure, democracy and politics, markets and economic systems, climate, and earthquakes—in fact, just about anything that can't be understood as sum of its parts and/or of which microscopic mechanisms are not exacly known can be seen as a complex system. As a complex systems scientist, I prefer to look for commonalities and connections between these seemingly unrelated fields rather than studying each in isolation.

Network science is the body of research that models systems as networks—a mathematical object consisting of nodes and links. Nodes represent the components of the system, and links represent the interaction between them. This simplification and abstraction allows us to focus on how elements are connected and what the connection patterns mean for the behavior of the system. Although network science is a relatively new discipline, it has become a cornerstone of complex systems research because it provides a powerful toolkit for studying diverse systems. 

Updates

• [2025-08-27] Our paper was published in Physical Review E:
  Block-corrected Modularity for Community Detection. 

• [2025-08-14] We have a new preprint on arXiv:
  Hierarchical organization of bursty trains in event sequences.

• [2025-07-10] Our paper was published in PNAS:
  Strength and weakness of disease-induced herd immunity in networks.

• [2025-06-05] Our paper was published in PLOS One:
  Geospatial analysis of toponyms in geotagged social media posts.

• [2025-06-05] I gave a talk at NetSci 2025 in Maastricht, the Netherlands:
  Disentangling epidemics and percolation.

• [2025-01-20] Our paper was published in Evolutionary Human Sciences:
  Close and more distant relatives are associated with child mortality risk in historical Finland.

• [2024-09-04] I gave a talk at Conference on Complex Systems 2024 in Exeter, UK:
  Strength and weakness of disease-induced herd immunity.

• [2024-04-25] I gave a talk at CompleNet 2024 in Exeter, UK:
  The strength and weakness of disease-induced herd immunity.

• [2023-09-24] I gave an online talk at the International Symposium and Workshop “Compiling GIS for Integrating Linguistic and Non-linguistic Information” organized by the National Museum of Ethnology, Japan:
  Geospatial Analysis of Toponyms in Geotagged Tweets.

• [2023-07-12] I gave a talk at NetSci 2023 in Vienna, Austria:
  Strength and weakness of disease-induced herd immunity.

• [2022-12-05] Our paper was published in Travel Behaviour and Society:
  Estimating inter-regional mobility during disruption: Comparing and combining different data sources.

• [2022-10-18] I gave a talk at the Conference on Complex Systems 2022 in Palma de Mallorca, Spain:
  Herd immunity and epidemic size in networks with vaccination homophily. 

• [2022-05-12] Our paper was published in Physical Review E:
  Herd immunity and epidemic size in networks with vaccination homophily.

• [2022-04-07] Our paper was published in PLOS Computational Biology:
  Adaptive and optimized COVID-19 vaccination strategies across geographical regions and age groups.

• [2021-10-25] I gave a talk at the Conference on Complex Systems 2021 in Lyon, France:
  Vaccination strategies for minimizing the number of deaths from emerging diseases. 

• [2021-07-26] Our paper was published in Physical Review E:
  Individual-driven versus interaction-driven burstiness in human dynamics: The case of Wikipedia edit history.

• [2021-07-08] I gave an online talk at Networks 2021:
  Vaccination strategies for minimizing the number of deaths from emerging diseases.

• [2020-09-25] I gave an online talk at NetSci 2020:
  Burst-tree decomposition of time series reveals the structure of temporal correlations.

• [2020-07-22] Our paper was published in Scientific Reports:
  Burst-tree decomposition of time series reveals the structure of temporal correlations.

• [2020-05-24] Our paper was published in Northeast Journal of Complex Systems (NEJCS):
  Waiting-Time Paradox in 1922.

• [2020-04-24] Our paper was published in Physical Review Research:
  Modeling temporal networks with bursty activity patterns of nodes and links.

• [2020-02-01] I started working as a postdoctoral researcher at Aalto University, Finland.

• [2020-01-20] I gave a talk at NetSci-X 2020 in Tokyo, Japan:
  Genealogical network analysis of social group evolution.