pynetflow : Python network Ricci curvature and flow

This repository contains the Python package called pynetflow, which enables the computation of Ricci curvature and Ricci flow. It also provides visualization capabilities for the network and its curvature throughout the flow process. Additionally, it implements a function to compute Ricci curvature on simplicial complexes and visualize the curvature of various cells based on their order.

Installation

$ python setup.py install

Library Codes

• ricci_curvature.py : This library contains the functions to compute the Forman-Ricci curvature on a simplicial complexes. The Forman-Ricci curvature is calculated for every cell, regardless of its orderomputed for every cells whatever their order.
• ricci_flow.py : This library contains the functions to compute the Forman-Ricci curvature on a network, and to run the Forman-Ricci flow on this network.
• ricci_vis.py : This library contains the functions for visualizing the Forman-Ricci curvature on simplicial complexes. Users can utilize the visualize_order function to display the network and curvature for a specific order, or employ the visualize_all function to display the network and curvature for every order. Additionally, this library includes a function to display the curvature evolution of the network during the flow process and generate a video documenting the flow.

Data

toy_network.csv : Adjacency matrix for a small network with a single connected component of 44 nodes

toy_data.csv : A data matrix of 10 columns (samples) and 44 rows (each corresponding to e.g. gene expression of a node of the above adj mat)

Usage

Ricci curvature and visualisation

SC = xgi.SimplicialComplex()
SC.add_simplices_from([[3, 4, 5], [3, 5, 6], [6, 7, 8, 9], [1, 4, 10, 11, 2], [1, 3, 10, 11, 2], [1, 0]])
pos = xgi.barycenter_spring_layout(SC)

# For visualise only the curvature of nodes (order = 0)
visualize_order(SC, 0)

# For visualise only the curvature of edges (order = 1)
visualize_order(SC, 1)

# For visualise only the curvature of triangles (order = 2)
visualize_order(SC, 2)

Ricci flow

After having checked and/or modified the script parameters in accordance to your data, set the desired number of iterations and run the following Python code :

from ricci_flow import drop_weights, Forman_ricci, Signal_entropy, dist_mat
from ricci_flow import RicciFlow_normalised, Total_ricci_curvature

adj = pd.read_csv('data/toy_network.csv', index_col = 0)
adj.columns = list(adj.index)
G = nx.from_pandas_adjacency(adj)
drop_weights(G)
vec = pd.read_csv('data/toy_data.csv', index_col = 0)

ve_init = np.array(vec['V5'])
ve_final = np.array(vec['V7'])
eta = 0.5
n_iter = 20

ricciflow = RicciFlow_normalised(G, ve_init, ve_final, Niter = n_iter, eta = eta)

The pynetflow documentation is hosted at ReadTheDocs.

Pynetflow is maintained by Anthony Baptista (anthony dot baptista at qmul dot ac dot uk)