This repository contains the code for the project "Modelling Higher-Order Network Dynamics in the Presence of Triadic Interactions" by Jun Yamamoto. The project was submitted as a part of the requirements for the degree of MSc in Mathematics at Queen Mary University of London. The project was supervised by Prof. Dr. Ginestra Bianconi.
The project consists of the numerical simulations of node dynamics on networks with triadic interactions, and the analysis of the results. The codes were written in Python 3 and the following packages are required:
The code is released under the MIT license.
triadic_interactions.model :
NDwTIs : Class for numerical simulations of node dynamics on networks with triadic interactions.
triadic_interactions.computation :
create_node_edge_incidence_matrix(edge_list): Create a node-edge incidence matrix B from a given edge list.
extract_by_std(X, std=3.0): Extract the data within a given number of standard deviations from its mean.
freedman_diaconis_rule(data, power=1. / 3., factor=2.): Compute the number of bins using the Freedman-Diaconis rule.
_check_data_shape(data): Check the shape of the data.
_generate_bins(data, bins): Generate the bins.
estimate_pdf(data, bins='fd', method='kde'): Estimate the probability density function.
estimate_pdf_joint(data, bins='fd', method='kde'): Estimate the joint probability density function.
estimate_pmf(data, bins='fd', method='kde'): Estimate the probability mass function.
estimate_pmf_joint(data, bins='fd', method='kde'): Estimate the joint probability mass function.
estimate_mutual_information(X, Y, bins='fd', pmf_method='kde', method='kl-div'): Estimate the mutual information.
covariance(data): Compute the covariance.
conditional_correlation(X, Y, Z, bins='fd'): Compute the conditional correlation.
conditional_mutual_information(X, Y, Z, bins='fd', pmf_method='kde', method='kl-div'): Compute the conditional mutual information.
triadic_interactions.computation :
plot_timeseries(X, output_file, t_max, n_samples=1, separate=False, theory=None): Plot the timeseries.
plot_pdf(probs, bins, output_file, f_theory=None, logscale=False, parallel=False): Plot the probability distributions.
plot_covariance(cov, output_file, theory=None): Plot the covariance matrix.
plot_conditional_correlation(Xgrids, cond_corr, order, output_file, std=False, Xrange=None, theory=None, f_supplement=None, threshold=None): Plot the conditional correlation.
plot_conditional_mutual_information(Xgrids, cmi, order, output_file, std=False, Xrange=None, theory=None): Plot conditional mutual information.
The following example demonstrates how to use the NDwTIs class to simulate the node dynamics on networks with triadic interactions.
from triadic_interactions.model import NDwTIs, create_node_edge_incidence_matrix
# Node
n_nodes = 3
# Edge list
edge_list = [[2, 3]]
n_edges = len(edge_list)
# Incidence matrix for the structural network
B = create_node_edge_incidence_matrix(edge_list)
# Incidence matrix for the triadic interactions
K = np.array([[1, 0, 0]])
model = NDwTIs(
B=B, K=K, w_pos=2., w_neg=1.,
threshold=1e-3, alpha=.1, noise_std=1e-3,
x_init=np.zeros(n_nodes), dt=1e-2, t_max=100.
)
# Run the simulation
model.run()The author would like to thank Prof. Dr. Ginestra Bianconi for her guidance and support throughout the project.
The author also received assistance from Dr. Anthony Baptista in implementing the create_node_edge_incidence_matrix function in triadic_interaction.computation and the NDwTIs class in triadic_interaction.model.