SnarlPy

Introduction

The module 'snarlpy' is a python packages encompassing a set of class and method implementations for 'networkx' graphs, in order to calculate linking numbers of spatially intertwined networks and optimal cuts to topologically unlink them. Used and explained in the publication: arXiv:2208.11662

Installation

Via PyPi

pip install snarlpy

Usage

For theory and algorithm details see publication: arXiv:2208.11662 Let's create an intertwined, spatial network with the package's internal generator (here two ladders) and calculate the linking number matrices 'lk_mat' (cycle space) and 'p'(edge space). When we have done so compute the the priority matrices and plot the matrices diagnonal values onto the respective graphs' edges (visualising the important edges for intertwinedness).

import numpy as np
import snarlpy.edgePriority as spe
import snarlpy.tangledGenerators as tg

def update_priorityPlot(D, p):

    colors = []
    priority_mat = [np.dot(p,p.T), np.dot(p.T,p)]

    for i, k in enumerate(D.layer):
        k.edges['priority'] = np.round( np.diagonal(priority_mat[i]),10)
        colors.append(k.edges['priority'])
    kwargs = {
        'color_nodes': ['#030512','#030512'],
        'color_edges': colors,
        'colormap': ['BuGn','RdPu'],
        'axis': True
    }
    fig = D.plot_circuit('priority', **kwargs)
    fig.show()

    return fig

num_periods = 2
D = tg.createLabelCatenation(num_periods)
graph_sets = [k.G for k in D.layer]
p, lk_mat = spe.getEdgeLinkageOperator(graph_sets)
fig = update_priorityPlot(D, p)
fig.show()

The package also allows you to directly compute cut sets, to find the best way to topologically disentangle the networks. Calling this bit of code will repeatedly compute the priority matrices for both networks and remove edges of highest priority one by one (as displayed on the carton below).

import spe.edgePriority as spe
import tangledGenerators as tg

num_periods = 2
D = tg.createLabelHexagonHopfed_V4()
graph_sets = [k.G for k in D.layer]
init_cut_sets = [graph_sets[:], graph_sets[::-1]]
cut_lists = []
for ics in init_cut_sets:
    cut_lists.append(spe.cuttingEdgeAlgorithm(*ics))

Further examples on the usage and percularities of edge priorities and network linkage can be found in the notebook example included.

Requirements

kirchhoff==0.2.7
matplotlib==3.7.1
networkx==2.8.4
numpy==1.23.5
pandas==1.5.3
plotly==5.9.0
scipy==1.10.1

Acknowledgement

snarlpy written by Felix Kramer