# Higher-Order Network Analytics for Time Series Data

Graph analytics and (social) network analysis have become cornerstones of data science. They are widely applied to relational data studied in disciplines such as computer science, physics, systems biology, social science or economics. However, we are increasingly confronted with high-frequency, time-resolved data which not only tell us *who* is related to *whom*, but also *when* and *in which sequence* these relations occurred. The analysis of such data is still a challenge. A naive application of network analysis and modeling techniques discards information on the timing and ordering of relations, which is the foundation of so-called *causal or time-respecting paths*, i.e. it is needed to answer the question *who* can influence *whom*. In my research, I study the effects of temporal ordering in time-resolved relational data from real-world systems. Using a combination of information-theoretic and statistical methods, we could demonstrate that temporal correlations in data from social and biological systems break the transitivity of causal paths. We further showed that the **application of network-based data analysis and modeling techniques as well as algebraic methods to time-stamped data yields wrong results**.

Addressing the problem that common graphical representations of relational data discard information on the temporal ordering of relations, we **developed a data analysis framework based on higher-order graphical models**. Extending the common network perspective, it allows to combine information on both topological and temporal characteristics of time-resolved relational data into compact probabilistic graphical models. This approach provides new ways to (i) model dynamical processes like diffusion, cascades or epidemic spreading, (ii) detect temporal-topological clusters based on higher-order Laplacians and spectral methods, (iii) assess the importance of nodes, and (iv) study the controllability of complex systems. This research aims at methodological advances which not only provide us with novel data mining techniques, but whose impact reaches beyond computer science, with applications in the modeling of complex systems in physics, systems biology, social science and economics.

## Exemplary publications

- R Lambiotte, M Rosvall, I Scholtes: From Networks to Optimal Higher-Order Models of Complex Systems, to appear, arXiv 1806.05977, February 2019
- I Scholtes:
- Y Zhang, A Garas and I Scholtes: Controllability of temporal networks: An analysis using higher-order networks. Under Review, arXiv 1701.06331, January 2017
- I Scholtes, N Wider, A Garas: Higher-Order Aggregate Networks in the Analysis of Temporal Networks: Path structures and centralities, European Physical Journal B, March 2016
- I Scholtes, N Wider, R Pfitzner, A Garas, CJ Tessone, F Schweitzer: Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks, Nature Communications, September 2014
- R Pfitzner, I Scholtes, A Garas, CJ Tessone, F Schweitzer: Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks, Physical Review Letters, May 2013