Network-based data mining techniques such as graph mining, (social) network analysis, link prediction and graph clustering form an important foundation for data science applications in computer science, computational social science, and the life sciences. They help to detect patterns in large data sets that capture dyadic relations between pairs of genes, species, humans, or documents and they have improved our understanding of complex networks.

While the potential of analysing graph or network representations of relational data is undisputed, we increasingly have access to data on networks that contain more than just dyadic relations. Consider, e.g., data on user click streams in the Web, time-stamped social networks, gene regulatory pathways, or time-stamped financial transactions. These are examples for time-resolved or sequential data that not only tell us who is related to whom but also when and in which order relations occur. Recent works have exposed that the timing and ordering of relations in such data can introduce higher-order, non-dyadic dependencies that are not captured by state-of-the-art graph representations. This oversimplification questions the validity of graph mining techniques in time series data and poses a threat for interdisciplinary applications of network analytics.

To address this challenge, researchers have developed advanced graph modelling and representation techniques based on higher- and variable-order Markov models, which enable us to model non-Markovian characteristics in time series data on networks. Introducing this exciting research field, the goal of this tutorial is to give an overview of cutting-edge higher-order data analytics techniques. Key takeaways for attendees will be (i) hands-on experience with higher-order network analytics, model selection, and data visualisation, and (ii) a demonstration of the benefits of higher-order network analytics in real time series data on social systems.


Anton Eriksson
Complex Systems Group
Department of Physics
Umeå University, SE

Jürgen Hackl
Assistant Professor
Department of Civil Engineering and Industrial Design
School of Engineering
University of Liverpool, UK


Participants should bring a laptop with a python 3.x environment. For the Session 1, a Python installation with jupyter, numpy, numba, pandas, sklearn and matplotlib (Optionally Docker and docker-compose). is required. For pathpy the setup instructions can be found here. Prior exposure to python is beneficial.


Welcome Note and Tutorial Overvie

Session 1: Mapping higher-order network flows

Intro: Mapping higher-order network flows (20 min) > slides

Live Coding (40 min) > code

Unit Topic Time
1 Infomap 10 min
2 Sparse state networks 15 min
3 Model selection and community detection 15 min

Coffee Break

Session 2: Higher-order Network Analysis and Visualisation with pathpy

Intro: Higher-Order Network Analytics for Time Series Data (15 min) > slides

Live Coding (40 min) > code

Unit Topic Time
1 Introduction to pathpy 10 min
2 (Spatial)-Temporal Network Analysis and Visualisation in pathpy 10 min
3 Higher-order Models of Paths 10 min
4 Multi-order Model Selection 10 min