An Eigenmodel for Dynamic Multilayer Networks

Author: Joshua D. Loyal

This package provides an interface for the model described in "An Eigenmodel for Dynamic Multilayer Networks". Inference is performed using coordinante ascent variational inference. For more details, see Loyal and Chen (2021).

Dependencies

multidynet requires:

• Python (>= 3.10)

and the requirements highlighted in requirements.txt. To install the requirements, run

pip install -r requirements.txt

Installation

You need a working installation of numpy, scipy, and Cython to install multidynet. Install these required dependencies before proceeding. Use the following commands to get the copy from GitHub and install all the dependencies:

>>> git clone https://github.com/joshloyal/multidynet.git
>>> cd multidynet
>>> pip install -r requirements.txt
>>> python setup.py install

Example

import matplotlib.pyplot as plt

from multidynet import DynamicMultilayerNetworkLSM
from multidynet.datasets import load_icews
from multidynet.plots import plot_latent_space


# load ICEWS data set (4 layers, 12 months and 65 countries)
Y, countries, layer_labels, time_labels = load_icews(dataset='small')
Y.shape
# >>> (4, 12, 65, 65)

# fit the model
model = DynamicMultilayerNetworkLSM(max_iter=500, n_features=2, init_type='svt')
model.fit(Y)

# extract the homophily coefficients (all positive)
print(model.lambda_)
# [[1.         1.        ]
#  [0.93377735 0.82923015]
#  [1.20083304 1.40344605]
#  [1.06239543 1.30391721]]

# plot the shared latent space
fig, ax = plt.subplots(figsize=(20, 6), ncols=2)

# January 2016
k = 0
t = 0
plot_latent_space(Y[k, t], model.Z_[t], X_sigma=model.Z_sigma_[t],
                   with_labels=True, font_size=10,
                   contour_alpha=0.1, n_std=1,
                   size=0, edge_width=0,
                   node_labels=countries,
                   ax=ax[0])
ax[0].axhline(0, linestyle='--', c='k')
ax[0].axvline(0, linestyle='--', c='k')
ax[0].set_xlabel('Dimension 1')
ax[0].set_ylabel('Dimension 2')
ax[0].set_title(time_labels[t])

# December 2016
k = 0
t = 11
plot_latent_space(Y[k, t], model.Z_[t], X_sigma=model.Z_sigma_[t],
                   with_labels=True, font_size=10,
                   contour_alpha=0.1, n_std=1,
                   size=0, edge_width=0,
                   node_labels=countries,
                   ax=ax[1])
ax[1].axhline(0, linestyle='--', c='k')
ax[1].axvline(0, linestyle='--', c='k')
ax[1].set_xlabel('Dimension 1')
ax[1].set_ylabel('Dimension 2')
ax[1].set_title(time_labels[t])

plt.show()

Simulation Studies and Real-Data Applications

The scripts directory includes the simulation studies and real-data applications found in the main article.