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Using Time-Aware Graph Neural Networks to Predict Temporal Centralities in Dynamic Graphs

Franziska Heeg, Ingo Scholtes

TL;DR

This work studies the application of De Bruijn Graph Neural Networks (DBGNN), a time-aware graph neural network architecture, to predict temporal path-based centralities in time series data and shows that it considerably improves the prediction of betweenness and closeness centrality.

Abstract

Node centralities play a pivotal role in network science, social network analysis, and recommender systems. In temporal data, static path-based centralities like closeness or betweenness can give misleading results about the true importance of nodes in a temporal graph. To address this issue, temporal generalizations of betweenness and closeness have been defined that are based on the shortest time-respecting paths between pairs of nodes. However, a major issue of those generalizations is that the calculation of such paths is computationally expensive. Addressing this issue, we study the application of De Bruijn Graph Neural Networks (DBGNN), a time-aware graph neural network architecture, to predict temporal path-based centralities in time series data. We experimentally evaluate our approach in 13 temporal graphs from biological and social systems and show that it considerably improves the prediction of betweenness and closeness centrality compared to (i) a static Graph Convolutional Neural Network, (ii) an efficient sampling-based approximation technique for temporal betweenness, and (iii) two state-of-the-art time-aware graph learning techniques for dynamic graphs.

Using Time-Aware Graph Neural Networks to Predict Temporal Centralities in Dynamic Graphs

TL;DR

This work studies the application of De Bruijn Graph Neural Networks (DBGNN), a time-aware graph neural network architecture, to predict temporal path-based centralities in time series data and shows that it considerably improves the prediction of betweenness and closeness centrality.

Abstract

Node centralities play a pivotal role in network science, social network analysis, and recommender systems. In temporal data, static path-based centralities like closeness or betweenness can give misleading results about the true importance of nodes in a temporal graph. To address this issue, temporal generalizations of betweenness and closeness have been defined that are based on the shortest time-respecting paths between pairs of nodes. However, a major issue of those generalizations is that the calculation of such paths is computationally expensive. Addressing this issue, we study the application of De Bruijn Graph Neural Networks (DBGNN), a time-aware graph neural network architecture, to predict temporal path-based centralities in time series data. We experimentally evaluate our approach in 13 temporal graphs from biological and social systems and show that it considerably improves the prediction of betweenness and closeness centrality compared to (i) a static Graph Convolutional Neural Network, (ii) an efficient sampling-based approximation technique for temporal betweenness, and (iii) two state-of-the-art time-aware graph learning techniques for dynamic graphs.
Paper Structure (25 sections, 6 equations, 4 figures, 18 tables)

This paper contains 25 sections, 6 equations, 4 figures, 18 tables.

Table of Contents

  1. Motivation
  2. Research Gap and Contributions
  3. Background and Related Work
  4. Dynamic Graphs and Time-respecting Paths
  5. Temporal Centralities
  6. Approximating Path-based Centralities
  7. A Time-Aware GNN to Predict Temporal Centralities
  8. Higher-Order De Bruijn Graph Models of Time-respecting paths
  9. De Bruijn Graph Neural Networks for Temporal Centrality Prediction
  10. Experimental Results
  11. Experimental setup
  12. Data sets
  13. Evaluation procedure
  14. Discussion of results
  15. Conclusion
  16. ...and 10 more sections

Figures (4)

  • Figure 1: Overview of proposed approach to predict temporal node centralities in a temporal graph: We consider a time-based split in a training and test graph (left). Calculating time-respecting paths in the training split enables us to (1) compute temporal centralities, and (2) fit a $k$-th order De Bruijn graph model for time-respecting paths. The weighted edges in such a $k$-th order De Bruin graph capture frequencies of time-respecting paths of length $k$ (see time-respecting path of length one (red) and two (magenta)). (3) We use these centralities and the k-th order models to train a De Bruijn graph neural network (DBGNN), which allows us to (4) predict temporal centralities in the test graph.
  • Figure 2: Static vs temporal betweenness centralities of all nodes in 13 empirical dynamic graphs
  • Figure 3: Static vs temporal closeness centralities of all nodes in 13 empirical dynamic graphs
  • Figure 4: Comparison of node embeddings generated by DBGNN model (top), GCN (middle), and EVO (bottom) for the eu-email-dept4 data set. Nodes are colored according to their temporal closeness (left) and betweenness (right) centrality.