multiNetX v1.0

multiNetX is a python package for the manipulation and visualization of multilayer networks. The core of this package is a MultilayerGraph, a class that inherits all properties from networkx.Graph().

This allows for:

• Creating networks with weighted or unweighted links (only undirected networks are supported in this version)
• Analysing the spectral properties of adjacency or Laplacian matrices
• Visualizing dynamical processes by coloring the nodes and links accordingly

How to install multiNetX

multinetx does not need intallation. You simply download the source files and save them into your file system. Then you have to add that directory to your PYTHONPATH. In Unix/Linux you can do this by writting in the terminal the following command:

export PYTHONPATH=path_to_your_python_libraries/multinetx:$PYTHONPATH

How to use multiNetX

Import standard libraries for numerics

import numpy as np

Import the package MultiNetX

import multinetx as mx

Create a multiplex 1st way

Create three Erd"os- R'enyi networks with N nodes for each layer

N = 5
g1 = mx.generators.erdos_renyi_graph(N,0.5,seed=218)
g2 = mx.generators.erdos_renyi_graph(N,0.6,seed=211)
g3 = mx.generators.erdos_renyi_graph(N,0.7,seed=208)

Create an 3Nx3N lil sparse matrix. It will be used to describe the layers interconnection

adj_block = mx.lil_matrix(np.zeros((N*3,N*3)))

Define the type of interconnection among the layers (here we use identity matrices thus connecting one-to-one the nodes among layers)

adj_block[0:  N,  N:2*N] = np.identity(N)    # L_12
adj_block[0:  N,2*N:3*N] = np.identity(N)    # L_13
adj_block[N:2*N,2*N:3*N] = np.identity(N)    # L_23
    
# use symmetric inter-adjacency matrix
adj_block += adj_block.T

Create an instance of the MultilayerGraph class

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3],
                        inter_adjacency_matrix=adj_block)

Weights can be added to the edges

mg.set_edges_weights(intra_layer_edges_weight=2,
                     inter_layer_edges_weight=3)

Create a multiplex 2nd way

mg = mx.MultilayerGraph()

Add layers

mg.add_layer(mx.generators.erdos_renyi_graph(N,0.5,seed=218))
mg.add_layer(mx.generators.erdos_renyi_graph(N,0.6,seed=211))
mg.add_layer(mx.generators.erdos_renyi_graph(N,0.7,seed=208))

Create an instance of the MultilayerGraph class

mg.layers_interconnect(inter_adjacency_matrix=adj_block)

Weights can be added to the edges

mg.set_edges_weights(intra_layer_edges_weight=2,
                     inter_layer_edges_weight=3)

The object mg inherits all properties from Graph of networkX, so that we can calculate adjacency or Laplacian matrices, their eigenvalues, etc.

How to plot multiplex networks

Import standard libraries

import numpy as np
import matplotlib.pyplot as plt

Import the package MultiNetX

import multinetx as mx

Create three Erd"os- R'enyi networks with N nodes for each layer

N = 50
g1 = mx.erdos_renyi_graph(N,0.07,seed=218)
g2 = mx.erdos_renyi_graph(N,0.07,seed=211)
g3 = mx.erdos_renyi_graph(N,0.07,seed=208)

Edge colored nertwork (no inter-connected layers)

Create the multiplex network

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3])

Set weights to the edges

mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_intra_edges_weights(layer=2,weight=3)

Plot the adjacency matrix and the multiplex networks

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(121)
ax1.imshow(mx.adjacency_matrix(mg,weight='weight').todense(),
		  origin='upper',interpolation='nearest',cmap=plt.cm.jet_r)
ax1.set_title('supra adjacency matrix')

ax2 = fig.add_subplot(122)
ax2.axis('off')
ax2.set_title('edge colored network')
pos = mx.get_position(mg,mx.fruchterman_reingold_layout(g1),
					  layer_vertical_shift=0.2,
					  layer_horizontal_shift=0.0,
					  proj_angle=47)
mx.draw_networkx(mg,pos=pos,ax=ax2,node_size=50,with_labels=False,
				 edge_color=[mg[a][b]['weight'] for a,b in mg.edges()],
				 edge_cmap=plt.cm.jet_r)
plt.show()

Regular interconnected multiplex

Define the type of interconnection between the layers

adj_block = mx.lil_matrix(np.zeros((N*3,N*3)))

adj_block[0:  N,  N:2*N] = np.identity(N)    # L_12
adj_block[0:  N,2*N:3*N] = np.identity(N)    # L_13
#adj_block[N:2*N,2*N:3*N] = np.identity(N)    # L_23
adj_block += adj_block.T

Create an instance of the MultilayerGraph class

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3], 
						inter_adjacency_matrix=adj_block)

mg.set_edges_weights(inter_layer_edges_weight=4)

mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_intra_edges_weights(layer=2,weight=3)

Plot the adjacency matrix and the multiplex networks

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(121)
ax1.imshow(mx.adjacency_matrix(mg,weight='weight').todense(),
		  origin='upper',interpolation='nearest',cmap=plt.cm.jet_r)
ax1.set_title('supra adjacency matrix')

ax2 = fig.add_subplot(122)
ax2.axis('off')
ax2.set_title('regular interconnected network')
pos = mx.get_position(mg,mx.fruchterman_reingold_layout(mg.get_layer(0)),
					  layer_vertical_shift=1.4,
					  layer_horizontal_shift=0.0,
					  proj_angle=7)
mx.draw_networkx(mg,pos=pos,ax=ax2,node_size=50,with_labels=False,
				 edge_color=[mg[a][b]['weight'] for a,b in mg.edges()],
				 edge_cmap=plt.cm.jet_r)
plt.show()

General multiplex multiplex

Define the type of interconnection between the layers

adj_block = mx.lil_matrix(np.zeros((N*4,N*4)))

adj_block[0  :  N ,   N:2*N] = np.identity(N)   # L_12
adj_block[0  :  N , 2*N:3*N] = np.random.poisson(0.005,size=(N,N))   # L_13
adj_block[0  :  N , 3*N:4*N] = np.random.poisson(0.006,size=(N,N))   # L_34
adj_block[3*N:4*N , 2*N:3*N] = np.random.poisson(0.008,size=(N,N))   # L_14
adj_block += adj_block.T
adj_block[adj_block>1] = 1

Create an instance of the MultilayerGraph class

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3,g1],
						inter_adjacency_matrix=adj_block)

mg.set_edges_weights(inter_layer_edges_weight=5)

mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_intra_edges_weights(layer=2,weight=3)
mg.set_intra_edges_weights(layer=3,weight=4)

Plot the adjacency matrix and the multiplex networks

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(121)
ax1.imshow(mx.adjacency_matrix(mg,weight='weight').todense(),
		  origin='upper',interpolation='nearest',cmap=plt.cm.jet_r)
ax1.set_title('supra adjacency matrix')

ax2 = fig.add_subplot(122)
ax2.axis('off')
ax2.set_title('general multiplex network')
pos = mx.get_position(mg,mx.fruchterman_reingold_layout(mg.get_layer(0)),
					  layer_vertical_shift=.3,
					  layer_horizontal_shift=0.9,
					  proj_angle=.2)
mx.draw_networkx(mg,pos=pos,ax=ax2,node_size=50,with_labels=False,
				 edge_color=[mg[a][b]['weight'] for a,b in mg.edges()],
				 edge_cmap=plt.cm.jet_r)
plt.show()

Copyright

(C) Copyright 2013-2015, Nikos E Kouvaris

Each file in this folder is part of the multiNetX package.

multiNetX is part of the deliverables of the LASAGNE project (multi-LAyer SpAtiotemporal Generalized NEtworks), EU/FP7-2012-STREP-318132 (http://complex.ffn.ub.es/~lasagne/)

multiNetX is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

multiNetX is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.