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

The easy way (see https://pypi.org/project/multinetx/). Simply, open your terminal and write:

 pip install multinetx

Otherwise, you simply download/clone the source files into the directory you keep your python scripts. Then you add that directory to your PYTHONPATH. In Unix/Linux you can do this by adding into your .bashrc file the two following lines:

export PYTHONPATH=/home/your_username/your_python_libs:$PYTHONPATH
export PYTHONPATH=/home/your_username/your_python_libs/multinetx:$PYTHONPATH

After request of some users I give here an example of how to "install" multinetx:

Create a directory for your python libraries (if you do not have already)

mkdir your_python_libs

Enter this directory

cd your_python_libs

Clone the multinetx

git clone https://github.com/nkoub/multinetx.git

Add multinetx to your PYTHONPATH by adding to your .bashrc the two following lines:

export PYTHONPATH=/home/your_username/your_python_libs:$PYTHONPATH
export PYTHONPATH=/home/your_username/your_python_libs/multinetx:$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()

How to plot 3D multiplex networks

Import specific libraries

import numpy as np #  to use matrix
import matplotlib.pyplot as plt # to use plot
import networkx as nx # to use graphs
import multinetx as mx # to use multinet
import math # to use floor
import matplotlib.cm as cmx # to use cmap (for data color values)
import matplotlib.colors as colors # to use cmap (for data color values)
import matplotlib.cbook as cb # to test if an object is a string

from mpl_toolkits.mplot3d import Axes3D # to use 3D plot

Create multinet

N1 = 10
g1 = nx.cycle_graph(N1)
N2 = 2*N1
g2 = nx.cycle_graph(N2)

adj_block = mx.lil_matrix(np.zeros((N1+N2,N1+N2)))

for i in range(N1):
    adj_block[i,N1+2*i] = 1

adj_block += adj_block.T

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

Plot multiplex networks by layer

# Create the figure
fig = plt.figure()
# Create 3D axes
ax = fig.add_subplot(111, projection='3d')

pos = mx.get_position3D(mg)


intra_c = ['b','r']
inter_c = 'grey'
layer_c = ['b','r']

mg.set_edges_weights(inter_layer_edges_weight=1, intra_layer_edges_weight=1)
edge_color=[mg[a][b]['weight'] for a,b in mg.edges()]


mx.FigureByLayer(mg, pos, ax, intra_edge_color=intra_c,node_color=layer_c, inter_edge_color=inter_c)
ax.axis('off')

(-1.0999999812245371,
 1.0999999991059304,
 -1.0999999595281706,
 1.0999999980727702)

Plot multiplex networks by nodes and edges

# Create the figure
fig = plt.figure()
# Create 3D axes
ax = fig.add_subplot(111, projection='3d')
# Get position of all nodes
pos = mx.get_position3D(mg)
# Set edges weights
mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_edges_weights(inter_layer_edges_weight=3)

# Get edges and nodes color
edge_color=[mg.edges.get((a,b))['weight'] for a,b in mg.edges()]
node_color=[i for i in mg.nodes]

# Plot multiplex network using options
mx.Figure3D(mg, pos, ax, edge_color=edge_color, node_color=node_color, 
         node_shape = 'D', edge_linewidth = 0.5, node_linewidth = 0,
         edge_style = 'dashed', label = 'Node', with_labels = True,
         font_size = 8, font_color = 'red', font_weight = 'heavy', 
         font_family = 'fantasy')
# Print legend
ax.legend(scatterpoints=1)

/home/icarrasco/fnh_k/multinetx_display/multinetx/draw.py:439: MatplotlibDeprecationWarning: The is_string_like function was deprecated in version 2.1.
  if not cb.is_string_like(label):





<matplotlib.legend.Legend at 0x7fcc9b69fbe0>

Plot partial multiplex networks by nodes and edges

# Create the figure
fig = plt.figure()
# Create 3D axes
ax = fig.add_subplot(111, projection='3d')

# Get position of nodes
pos = mx.get_position3D(mg)
# Choose some edges
edge_list = [(0, 1),(0, 10),(0, 9),(1, 2),(1, 12),(2, 3),(2, 14),(3, 16),(3, 4),(4, 18),(4, 5),(5, 20),(5, 6),(6, 22),(6, 7),(7, 8),(7, 24)]
# Choose the edges color
edge_color = [np.random.randint(1,100) for i in edge_list]
# Choose some nodes
node_list = [0,2,4,6,8,10,12,14,16,18,20]
# Choose the nodes color
node_color = [0,2,4,6,8,10,12,14,16,18,20]
# Plot the partial mutiplex network
mx.Figure3D(mg, pos, ax, node_list=node_list, node_color=node_color, edge_list=edge_list, edge_color = edge_color)

How to cite multiNetX

If multiNetX was useful and facilitated your research and work flow you can use a reference in your publications by citing either of the following papers for which multiNetX was originally developed:

R. Amato, N. E Kouvaris, M. San Miguel and A. Diaz-Guilera, Opinion competition dynamics on multiplex networks, New J. Phys. DOI: https://doi.org/10.1088/1367-2630/aa936a
N. E. Kouvaris, S. Hata and A. Diaz-Guilera, Pattern formation in multiplex networks, Scientific Reports 5, 10840 (2015). http://www.nature.com/srep/2015/150604/srep10840/full/srep10840.html
A. Sole-Ribata, M. De Domenico, N. E. Kouvaris, A. Diaz-Guilera, S. Gomez and A. Arenas, Spectral properties of the Laplacian of a multiplex network, Phys. Rev. E 88, 032807 (2013). http://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.032807

Copyright

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/.

Name		Name	Last commit message	Last commit date
Latest commit History 62 Commits
.ipynb_checkpoints		.ipynb_checkpoints
classes		classes
create_multiplex_files		create_multiplex_files
dynamics		dynamics
guide		guide
multinetx		multinetx
plot_multiplex_networks_files		plot_multiplex_networks_files
spectrum_two_layers_files		spectrum_two_layers_files
.gitignore		.gitignore
README.md		README.md
README.md~		README.md~
__init__.py		__init__.py
create_multiplex.ipynb		create_multiplex.ipynb
create_multiplex.md		create_multiplex.md
draw.py		draw.py
exceptions.py		exceptions.py
logo.png		logo.png
logo.svg		logo.svg
multinetX_test.ipynb		multinetX_test.ipynb
plot_multiplex_networks.ipynb		plot_multiplex_networks.ipynb
plot_multiplex_networks.md		plot_multiplex_networks.md
spectrum_two_layers.ipynb		spectrum_two_layers.ipynb
spectrum_two_layers.md		spectrum_two_layers.md
utilities.py		utilities.py

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multiNetX v1.0

How to install multiNetX

How to use multiNetX

Import standard libraries for numerics

Import the package MultiNetX

Create a multiplex 1st way

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

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

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

Create an instance of the MultilayerGraph class

Weights can be added to the edges

Create a multiplex 2nd way

Add layers

Create an instance of the MultilayerGraph class

Weights can be added to the edges

How to plot multiplex networks

Import standard libraries

Import the package MultiNetX

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

Edge colored nertwork (no inter-connected layers)

Create the multiplex network

Set weights to the edges

Plot the adjacency matrix and the multiplex networks

Regular interconnected multiplex

Define the type of interconnection between the layers

Create an instance of the MultilayerGraph class

Plot the adjacency matrix and the multiplex networks

General multiplex multiplex

Define the type of interconnection between the layers

Create an instance of the MultilayerGraph class

Plot the adjacency matrix and the multiplex networks

How to plot 3D multiplex networks

Import specific libraries

Create multinet

Plot multiplex networks by layer

Plot multiplex networks by nodes and edges

Plot partial multiplex networks by nodes and edges

How to cite multiNetX

Copyright

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