The document discusses a two-step approach to predicting dynamic networks, particularly focusing on social media and energy networks. It outlines methods for forecasting the number of new nodes and their connections, and optimizing the allocation of network edges using flux balance analysis. The findings underscore the complexity of accurately forecasting and optimizing dynamic networks due to the potential emergence of new nodes and edges.

1. Australia’s National Science Agency
Predicting dynamic networks
Sevvandi Kandanaarachchi, Ziqi Xu and Stefan Westerlund
WIMSIG 2024

2. • Social media networks
• New connections
• Energy networks
Dynamic networks?

3. • Social media networks
• New connections
• Energy networks
Dynamic networks?

4. Can we predict/forecast a dynamic
network at a future time step?

5. 𝑡 = 1
𝑡 = 2 𝑡 = 3
𝑡 = 4
𝑡 = 5
𝑡 = 6 𝑡 = 7 𝑡 = 8

6. • Link prediction
• Given the network, does this link/edge exist?
• Does not forecast the network structure
• Train algorithm on some existing links and predict others
• Forecasting the entire network is different
• We don’t know the network at the next time point
• New nodes can come in
• New edges between existing nodes
• New edges between new nodes etc . . .
Related but different topics

7. Two step approach:
Forecast & Optimize

8. • Use standard time series methods (ARIMA)
• Forecast the number of new nodes at 𝑇 + ℎ
• For existing nodes forecast the degree
• Degree: the number of edges it connects to
• Eg. { 1, 3, 7, 8, 10, 15, 16, 16, . . . }
• What about new nodes?
• For each network at time 𝑡 look at the new nodes
• Find their degree
• What is the new nodes degree like?
• Treat that as the forecast degree for new nodes
Step 1: Forecasting

9. 𝑡 = 1
𝑡 = 2 𝑡 = 3
𝑡 = 4
𝑡 = 5
𝑡 = 6 𝑡 = 7 𝑡 = 8

10. • We have estimates for
• Number of nodes in the graph
• Degree of existing nodes
• Degree of new nodes
• For each of these we have 𝑁 𝜇, 𝜎!
What we know about the next time step
Degree forecast

11. Australia’s National Science Agency
Question: How to allocate the degrees
(edges) among all the nodes?

12. Optimize: Flux Balance Analysis
used in metabolic network
reconstruction

13. Flux Balance
Analysis
Figure taken from
Orth, J., Thiele, I. & Palsson, B.
What is flux balance analysis?.
Nat Biotechnol 28, 245–248 (2010).
https://doi.org/10.1038/nbt.1614

14. • We solve an optimization problem
• Each edge is a variable 𝑒"# - this is what we’re trying to find
• Each edge has a weight 𝜉"#
• If the edge is seen in the recent past is has a higher weight
• If not – lower weight
• Possible new edges from new nodes – another weight
• Have different weight schemes
– Linearly/harmonically decaying weights in time
• Maximize 𝜉"#𝑒"# subject to constraints
Step 2: Adapted Flux Balance Analysis

15. • Maximize 𝜉"#𝑒"#
• Subject to degree constraints
• 𝑑! ≤ 𝑐!
• Where 𝑐! is the forecast degree of node 𝑖
• What it does
• Allocates these edges in a way that maximizes the objective function
• Because we’re using the node degrees at a future time step
• We forecast the network
Optimization problem

16. Forecast and optimize strategy!

17. Example Graph forecasts
1 timestep ahead 3 timesteps ahead 5 timesteps ahead

18. • Comparison of forecast with actual and other details in paper
• https://arxiv.org/abs/2401.04280
• R package netseer on CRAN
Other details
Preprint QR code

19. • Applications in your domain?
• Thoughts?
Input from you …

20. Australia’s National Science Agency
Thank you!