Overcoming the complexity barrier of the dynamic message-passing method in networks with fat-tailed degree distributions
Dynamics of agents on network is characterised by the interplay between (thermal) noise and interaction, the balance between the two has deep effects on the states of the agents. We study the linear threshold model on a random network with direct coupling: , where
and
are the noise and interaction term respectively.
We develop an analytical method that performes the average over the noise, so you get the activation probability of each node of the network. However, performing this average requires sampling from a huge space. This contribution provides an efficient way to solve this problem using dynamic programming. Check out our article or the preprint for more. This repository provides the code to reproduce the results of the manuscrip.
You need python and jupyter notebook installed in your system. Important files are:
- power.py: python script
- analyse_results.ipynb
power.py is a Python script that runs the cavity method on a network with power law degree distribution and stores the output files inside a folder /data. Run it first from a terminal by typing python power.py
analyse_results.ipynb is a Jupyter notebook that loads the output files from the script and create the heatmap of Fig. 2
The figure 2 in the letter explores different values of the noise level T. To reproduce the results, the evaluation associated to each value of T is run in parallel. You can control how many processes to be run in parallel, run python power.py -h in a terminal to know more.
N.B.
Default parameter of power.py are chosen to complete the evaluation in a reasonable time. However, If you want to reproduce the figure of the manuscript, run
python power.py -N 200000 --Ts 0.01 1.1 0.01
